Make 1998 using the least possible digits 8Expressing numbers using 0, 1, 2, 3, and 4Make numbers 1 - 32 using the digits 2, 0, 1, 7How many consecutive integers can you make using only four digits?Make numbers 1 - 30 using the digits 2, 0, 1, 8Make numbers 93 using the digits 2, 0, 1, 8Make numbers 1-30 using 2, 0, 1, 9Make all the onesFind 2018 with the least amount of numbersCreate the numbers 1 - 30 using the digits 2, 0, 1, 9 in this particular order!

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Make 1998 using the least possible digits 8


Expressing numbers using 0, 1, 2, 3, and 4Make numbers 1 - 32 using the digits 2, 0, 1, 7How many consecutive integers can you make using only four digits?Make numbers 1 - 30 using the digits 2, 0, 1, 8Make numbers 93 using the digits 2, 0, 1, 8Make numbers 1-30 using 2, 0, 1, 9Make all the onesFind 2018 with the least amount of numbersCreate the numbers 1 - 30 using the digits 2, 0, 1, 9 in this particular order!






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








8












$begingroup$


Make the number 1998 using the minimum amount of digits 8.



Your allowed operations are +, -, *, /, ^, % (percent).



You need not use only integers 8: 88 and the likes are acceptable.



This puzzle comes from an old friend's school DMs. He said the best that could be done was 10, so I'm turning to the community to see if you can do it better.



Have fun.










share|improve this question









New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$













  • $begingroup$
    Can we write two eights together to make 88?
    $endgroup$
    – Bass
    9 hours ago










  • $begingroup$
    @Andrew Viola! We have got it with 9 8's (by @HerbWolfe)
    $endgroup$
    – Quark-epoch
    8 hours ago







  • 1




    $begingroup$
    @Quark-epoch I got a nine-$8$ solution around 15 minutes before Herb Wolfe :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago










  • $begingroup$
    The real question is, what about 8 8s?
    $endgroup$
    – Andrew
    8 hours ago






  • 1




    $begingroup$
    Adding concatenation really does change the question.
    $endgroup$
    – Ben Barden
    7 hours ago

















8












$begingroup$


Make the number 1998 using the minimum amount of digits 8.



Your allowed operations are +, -, *, /, ^, % (percent).



You need not use only integers 8: 88 and the likes are acceptable.



This puzzle comes from an old friend's school DMs. He said the best that could be done was 10, so I'm turning to the community to see if you can do it better.



Have fun.










share|improve this question









New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$













  • $begingroup$
    Can we write two eights together to make 88?
    $endgroup$
    – Bass
    9 hours ago










  • $begingroup$
    @Andrew Viola! We have got it with 9 8's (by @HerbWolfe)
    $endgroup$
    – Quark-epoch
    8 hours ago







  • 1




    $begingroup$
    @Quark-epoch I got a nine-$8$ solution around 15 minutes before Herb Wolfe :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago










  • $begingroup$
    The real question is, what about 8 8s?
    $endgroup$
    – Andrew
    8 hours ago






  • 1




    $begingroup$
    Adding concatenation really does change the question.
    $endgroup$
    – Ben Barden
    7 hours ago













8












8








8





$begingroup$


Make the number 1998 using the minimum amount of digits 8.



Your allowed operations are +, -, *, /, ^, % (percent).



You need not use only integers 8: 88 and the likes are acceptable.



This puzzle comes from an old friend's school DMs. He said the best that could be done was 10, so I'm turning to the community to see if you can do it better.



Have fun.










share|improve this question









New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$




Make the number 1998 using the minimum amount of digits 8.



Your allowed operations are +, -, *, /, ^, % (percent).



You need not use only integers 8: 88 and the likes are acceptable.



This puzzle comes from an old friend's school DMs. He said the best that could be done was 10, so I'm turning to the community to see if you can do it better.



Have fun.







formation-of-numbers






share|improve this question









New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.










share|improve this question









New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








share|improve this question




share|improve this question








edited 8 hours ago







Andrew













New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 9 hours ago









AndrewAndrew

1414 bronze badges




1414 bronze badges




New contributor



Andrew is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor




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Check out our Code of Conduct.
















  • $begingroup$
    Can we write two eights together to make 88?
    $endgroup$
    – Bass
    9 hours ago










  • $begingroup$
    @Andrew Viola! We have got it with 9 8's (by @HerbWolfe)
    $endgroup$
    – Quark-epoch
    8 hours ago







  • 1




    $begingroup$
    @Quark-epoch I got a nine-$8$ solution around 15 minutes before Herb Wolfe :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago










  • $begingroup$
    The real question is, what about 8 8s?
    $endgroup$
    – Andrew
    8 hours ago






  • 1




    $begingroup$
    Adding concatenation really does change the question.
    $endgroup$
    – Ben Barden
    7 hours ago
















  • $begingroup$
    Can we write two eights together to make 88?
    $endgroup$
    – Bass
    9 hours ago










  • $begingroup$
    @Andrew Viola! We have got it with 9 8's (by @HerbWolfe)
    $endgroup$
    – Quark-epoch
    8 hours ago







  • 1




    $begingroup$
    @Quark-epoch I got a nine-$8$ solution around 15 minutes before Herb Wolfe :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago










  • $begingroup$
    The real question is, what about 8 8s?
    $endgroup$
    – Andrew
    8 hours ago






  • 1




    $begingroup$
    Adding concatenation really does change the question.
    $endgroup$
    – Ben Barden
    7 hours ago















$begingroup$
Can we write two eights together to make 88?
$endgroup$
– Bass
9 hours ago




$begingroup$
Can we write two eights together to make 88?
$endgroup$
– Bass
9 hours ago












$begingroup$
@Andrew Viola! We have got it with 9 8's (by @HerbWolfe)
$endgroup$
– Quark-epoch
8 hours ago





$begingroup$
@Andrew Viola! We have got it with 9 8's (by @HerbWolfe)
$endgroup$
– Quark-epoch
8 hours ago





1




1




$begingroup$
@Quark-epoch I got a nine-$8$ solution around 15 minutes before Herb Wolfe :-)
$endgroup$
– Rand al'Thor
8 hours ago




$begingroup$
@Quark-epoch I got a nine-$8$ solution around 15 minutes before Herb Wolfe :-)
$endgroup$
– Rand al'Thor
8 hours ago












$begingroup$
The real question is, what about 8 8s?
$endgroup$
– Andrew
8 hours ago




$begingroup$
The real question is, what about 8 8s?
$endgroup$
– Andrew
8 hours ago




1




1




$begingroup$
Adding concatenation really does change the question.
$endgroup$
– Ben Barden
7 hours ago




$begingroup$
Adding concatenation really does change the question.
$endgroup$
– Ben Barden
7 hours ago










8 Answers
8






active

oldest

votes


















8














$begingroup$

Found a solution with 8 eights, using concatenation and finally finding some use for the percent sign:




$$frac88 + 8times8 +8 -8% -8%8%$$
$$ = frac88 + 64 + 8 -.08 -.08.08 = frac160.08 - frac.08.08- frac.08.08 = 160*12.5 -2 = 1998$$




EDITED (much later..): Found another, without concatenation this time:




$$8 times (8+8) times (8+8) - frac88%+8% $$
$$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$







share|improve this answer











$endgroup$














  • $begingroup$
    After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
    $endgroup$
    – Bass
    7 hours ago











  • $begingroup$
    Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
    $endgroup$
    – Adam
    6 hours ago










  • $begingroup$
    @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
    $endgroup$
    – Bass
    6 hours ago










  • $begingroup$
    Ah, damn, I was so close. Well done.
    $endgroup$
    – Rand al'Thor
    5 hours ago






  • 2




    $begingroup$
    At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
    $endgroup$
    – im_so_meta_even_this_acronym
    3 hours ago


















4














$begingroup$

A solution with nine $8$s:




$$frac88+(8times8)+88% - frac8+88$$




i.e.




$1100 + 800 + 100 - 2$, taking advantage of the fact that $%$ is an allowed operation.




A very simple solution with ten $8$s (which I'm surprised nobody else has done):




$$frac88888 + 888 - frac88$$







share|improve this answer











$endgroup$














  • $begingroup$
    I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
    $endgroup$
    – Andrew
    8 hours ago










  • $begingroup$
    Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
    $endgroup$
    – Rand al'Thor
    8 hours ago











  • $begingroup$
    @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
    $endgroup$
    – Rand al'Thor
    8 hours ago










  • $begingroup$
    Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
    $endgroup$
    – Andrew
    8 hours ago






  • 1




    $begingroup$
    the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
    $endgroup$
    – Ben Barden
    7 hours ago


















4














$begingroup$

I have a solution with 12 8s




$((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$




Updated, another with 9 8s




$frac8888-88 + 888$







share|improve this answer











$endgroup$










  • 1




    $begingroup$
    I added some maths formatting - hope you don't mind :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago










  • $begingroup$
    Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
    $endgroup$
    – Rand al'Thor
    7 hours ago


















3














$begingroup$

Thanks to a comment from Ben Barden, here is another way of achieving 11 8s




$8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$







share|improve this answer











$endgroup$














  • $begingroup$
    If someone got 8 8s that'd be cool.
    $endgroup$
    – Andrew
    9 hours ago










  • $begingroup$
    you could pull the same trick I did, and shave it down to 11 as well.
    $endgroup$
    – Ben Barden
    9 hours ago











  • $begingroup$
    @BenBarden Thanks, totally missed that factorisation, +1 for you.
    $endgroup$
    – hexomino
    9 hours ago










  • $begingroup$
    ...and +1 back for being the originator of my solution's ancestor.
    $endgroup$
    – Ben Barden
    9 hours ago



















3














$begingroup$

Here's a solution with $9$ eights, without using the % operator:




$$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$







share|improve this answer









$endgroup$






















    3














    $begingroup$

    Here is a hilarious solution for 9




    $(frac8+88)^frac888-frac8(8+8)%=1998$




    For research purposes I'll also include my kinda illegal solution for 7




    $frac8+88(frac8.8%-frac88)=1998$







    share|improve this answer









    $endgroup$














    • $begingroup$
      You won... if we include the dot. I didn't allow the dot to be used but nice work still.
      $endgroup$
      – Andrew
      6 hours ago


















    2














    $begingroup$

    Stealing gloriously from the work of others, I have it down to 11:




    $(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$







    share|improve this answer











    $endgroup$














    • $begingroup$
      I added some maths formatting - hope you don't mind :-)
      $endgroup$
      – Rand al'Thor
      8 hours ago


















    1














    $begingroup$

    My first try, with ten:




    $frac88888 + 888 - frac88$




    Only 4 operators






    share|improve this answer








    New contributor



    Certainly not a dog is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.





    $endgroup$














    • $begingroup$
      This one is already in my answer. Nice one though!
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
      $endgroup$
      – Certainly not a dog
      7 hours ago










    • $begingroup$
      @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
      $endgroup$
      – Adam
      6 hours ago













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    8 Answers
    8






    active

    oldest

    votes








    8 Answers
    8






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    8














    $begingroup$

    Found a solution with 8 eights, using concatenation and finally finding some use for the percent sign:




    $$frac88 + 8times8 +8 -8% -8%8%$$
    $$ = frac88 + 64 + 8 -.08 -.08.08 = frac160.08 - frac.08.08- frac.08.08 = 160*12.5 -2 = 1998$$




    EDITED (much later..): Found another, without concatenation this time:




    $$8 times (8+8) times (8+8) - frac88%+8% $$
    $$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$







    share|improve this answer











    $endgroup$














    • $begingroup$
      After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
      $endgroup$
      – Bass
      7 hours ago











    • $begingroup$
      Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
      $endgroup$
      – Adam
      6 hours ago










    • $begingroup$
      @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
      $endgroup$
      – Bass
      6 hours ago










    • $begingroup$
      Ah, damn, I was so close. Well done.
      $endgroup$
      – Rand al'Thor
      5 hours ago






    • 2




      $begingroup$
      At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
      $endgroup$
      – im_so_meta_even_this_acronym
      3 hours ago















    8














    $begingroup$

    Found a solution with 8 eights, using concatenation and finally finding some use for the percent sign:




    $$frac88 + 8times8 +8 -8% -8%8%$$
    $$ = frac88 + 64 + 8 -.08 -.08.08 = frac160.08 - frac.08.08- frac.08.08 = 160*12.5 -2 = 1998$$




    EDITED (much later..): Found another, without concatenation this time:




    $$8 times (8+8) times (8+8) - frac88%+8% $$
    $$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$







    share|improve this answer











    $endgroup$














    • $begingroup$
      After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
      $endgroup$
      – Bass
      7 hours ago











    • $begingroup$
      Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
      $endgroup$
      – Adam
      6 hours ago










    • $begingroup$
      @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
      $endgroup$
      – Bass
      6 hours ago










    • $begingroup$
      Ah, damn, I was so close. Well done.
      $endgroup$
      – Rand al'Thor
      5 hours ago






    • 2




      $begingroup$
      At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
      $endgroup$
      – im_so_meta_even_this_acronym
      3 hours ago













    8














    8










    8







    $begingroup$

    Found a solution with 8 eights, using concatenation and finally finding some use for the percent sign:




    $$frac88 + 8times8 +8 -8% -8%8%$$
    $$ = frac88 + 64 + 8 -.08 -.08.08 = frac160.08 - frac.08.08- frac.08.08 = 160*12.5 -2 = 1998$$




    EDITED (much later..): Found another, without concatenation this time:




    $$8 times (8+8) times (8+8) - frac88%+8% $$
    $$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$







    share|improve this answer











    $endgroup$



    Found a solution with 8 eights, using concatenation and finally finding some use for the percent sign:




    $$frac88 + 8times8 +8 -8% -8%8%$$
    $$ = frac88 + 64 + 8 -.08 -.08.08 = frac160.08 - frac.08.08- frac.08.08 = 160*12.5 -2 = 1998$$




    EDITED (much later..): Found another, without concatenation this time:




    $$8 times (8+8) times (8+8) - frac88%+8% $$
    $$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 6 hours ago

























    answered 7 hours ago









    BassBass

    36.4k4 gold badges90 silver badges209 bronze badges




    36.4k4 gold badges90 silver badges209 bronze badges














    • $begingroup$
      After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
      $endgroup$
      – Bass
      7 hours ago











    • $begingroup$
      Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
      $endgroup$
      – Adam
      6 hours ago










    • $begingroup$
      @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
      $endgroup$
      – Bass
      6 hours ago










    • $begingroup$
      Ah, damn, I was so close. Well done.
      $endgroup$
      – Rand al'Thor
      5 hours ago






    • 2




      $begingroup$
      At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
      $endgroup$
      – im_so_meta_even_this_acronym
      3 hours ago
















    • $begingroup$
      After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
      $endgroup$
      – Bass
      7 hours ago











    • $begingroup$
      Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
      $endgroup$
      – Adam
      6 hours ago










    • $begingroup$
      @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
      $endgroup$
      – Bass
      6 hours ago










    • $begingroup$
      Ah, damn, I was so close. Well done.
      $endgroup$
      – Rand al'Thor
      5 hours ago






    • 2




      $begingroup$
      At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
      $endgroup$
      – im_so_meta_even_this_acronym
      3 hours ago















    $begingroup$
    After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
    $endgroup$
    – Bass
    7 hours ago





    $begingroup$
    After checking the other answers, I'd like to add a particularly smug wave (Hi there!) to Rand's first answer in particular :-)
    $endgroup$
    – Bass
    7 hours ago













    $begingroup$
    Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
    $endgroup$
    – Adam
    6 hours ago




    $begingroup$
    Darn you beat me to your second solution! :P (my 9 solution is a derpy way to do yours)
    $endgroup$
    – Adam
    6 hours ago












    $begingroup$
    @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
    $endgroup$
    – Bass
    6 hours ago




    $begingroup$
    @Adam, I totally stole the way to make the 50 from your post, the unusual use of the parens and the percent sign caught my eye, and I realised you had invented a totally brilliant way of creating the 50 I remembered desperately needing an hour ago. (The upvote on your answer is mine, more would definitely be in order.)
    $endgroup$
    – Bass
    6 hours ago












    $begingroup$
    Ah, damn, I was so close. Well done.
    $endgroup$
    – Rand al'Thor
    5 hours ago




    $begingroup$
    Ah, damn, I was so close. Well done.
    $endgroup$
    – Rand al'Thor
    5 hours ago




    2




    2




    $begingroup$
    At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
    $endgroup$
    – im_so_meta_even_this_acronym
    3 hours ago




    $begingroup$
    At the time this comment was sent, there were 8 upvotes on the question, 8 upvotes on the answer, 8 8's used to create this answer, and 8 answers.
    $endgroup$
    – im_so_meta_even_this_acronym
    3 hours ago













    4














    $begingroup$

    A solution with nine $8$s:




    $$frac88+(8times8)+88% - frac8+88$$




    i.e.




    $1100 + 800 + 100 - 2$, taking advantage of the fact that $%$ is an allowed operation.




    A very simple solution with ten $8$s (which I'm surprised nobody else has done):




    $$frac88888 + 888 - frac88$$







    share|improve this answer











    $endgroup$














    • $begingroup$
      I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
      $endgroup$
      – Andrew
      8 hours ago










    • $begingroup$
      Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
      $endgroup$
      – Rand al'Thor
      8 hours ago











    • $begingroup$
      @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
      $endgroup$
      – Andrew
      8 hours ago






    • 1




      $begingroup$
      the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
      $endgroup$
      – Ben Barden
      7 hours ago















    4














    $begingroup$

    A solution with nine $8$s:




    $$frac88+(8times8)+88% - frac8+88$$




    i.e.




    $1100 + 800 + 100 - 2$, taking advantage of the fact that $%$ is an allowed operation.




    A very simple solution with ten $8$s (which I'm surprised nobody else has done):




    $$frac88888 + 888 - frac88$$







    share|improve this answer











    $endgroup$














    • $begingroup$
      I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
      $endgroup$
      – Andrew
      8 hours ago










    • $begingroup$
      Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
      $endgroup$
      – Rand al'Thor
      8 hours ago











    • $begingroup$
      @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
      $endgroup$
      – Andrew
      8 hours ago






    • 1




      $begingroup$
      the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
      $endgroup$
      – Ben Barden
      7 hours ago













    4














    4










    4







    $begingroup$

    A solution with nine $8$s:




    $$frac88+(8times8)+88% - frac8+88$$




    i.e.




    $1100 + 800 + 100 - 2$, taking advantage of the fact that $%$ is an allowed operation.




    A very simple solution with ten $8$s (which I'm surprised nobody else has done):




    $$frac88888 + 888 - frac88$$







    share|improve this answer











    $endgroup$



    A solution with nine $8$s:




    $$frac88+(8times8)+88% - frac8+88$$




    i.e.




    $1100 + 800 + 100 - 2$, taking advantage of the fact that $%$ is an allowed operation.




    A very simple solution with ten $8$s (which I'm surprised nobody else has done):




    $$frac88888 + 888 - frac88$$








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 8 hours ago

























    answered 9 hours ago









    Rand al'ThorRand al'Thor

    75.4k15 gold badges248 silver badges498 bronze badges




    75.4k15 gold badges248 silver badges498 bronze badges














    • $begingroup$
      I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
      $endgroup$
      – Andrew
      8 hours ago










    • $begingroup$
      Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
      $endgroup$
      – Rand al'Thor
      8 hours ago











    • $begingroup$
      @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
      $endgroup$
      – Andrew
      8 hours ago






    • 1




      $begingroup$
      the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
      $endgroup$
      – Ben Barden
      7 hours ago
















    • $begingroup$
      I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
      $endgroup$
      – Andrew
      8 hours ago










    • $begingroup$
      Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
      $endgroup$
      – Rand al'Thor
      8 hours ago











    • $begingroup$
      @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
      $endgroup$
      – Andrew
      8 hours ago






    • 1




      $begingroup$
      the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
      $endgroup$
      – Ben Barden
      7 hours ago















    $begingroup$
    I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
    $endgroup$
    – Andrew
    8 hours ago




    $begingroup$
    I saw this puzzle on a site and thought to ask this SE about it. The given solution on the site had ten 8s, so this is technically an improvement. Nice work, Rand!
    $endgroup$
    – Andrew
    8 hours ago












    $begingroup$
    Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
    $endgroup$
    – Rand al'Thor
    8 hours ago





    $begingroup$
    Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
    $endgroup$
    – Rand al'Thor
    8 hours ago













    $begingroup$
    @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
    $endgroup$
    – Rand al'Thor
    8 hours ago




    $begingroup$
    @Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
    $endgroup$
    – Rand al'Thor
    8 hours ago












    $begingroup$
    Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
    $endgroup$
    – Andrew
    8 hours ago




    $begingroup$
    Well... I misremembered. It was not a real site. It was a DM with a friend in school. I'll make sure to mention this in an edit.
    $endgroup$
    – Andrew
    8 hours ago




    1




    1




    $begingroup$
    the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
    $endgroup$
    – Ben Barden
    7 hours ago




    $begingroup$
    the reason no one had done the "very simple solution" was that things like 88, 888, etc were not declared as permissible until relatively shortly before your answer.
    $endgroup$
    – Ben Barden
    7 hours ago











    4














    $begingroup$

    I have a solution with 12 8s




    $((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$




    Updated, another with 9 8s




    $frac8888-88 + 888$







    share|improve this answer











    $endgroup$










    • 1




      $begingroup$
      I added some maths formatting - hope you don't mind :-)
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
      $endgroup$
      – Rand al'Thor
      7 hours ago















    4














    $begingroup$

    I have a solution with 12 8s




    $((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$




    Updated, another with 9 8s




    $frac8888-88 + 888$







    share|improve this answer











    $endgroup$










    • 1




      $begingroup$
      I added some maths formatting - hope you don't mind :-)
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
      $endgroup$
      – Rand al'Thor
      7 hours ago













    4














    4










    4







    $begingroup$

    I have a solution with 12 8s




    $((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$




    Updated, another with 9 8s




    $frac8888-88 + 888$







    share|improve this answer











    $endgroup$



    I have a solution with 12 8s




    $((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$




    Updated, another with 9 8s




    $frac8888-88 + 888$








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 8 hours ago

























    answered 9 hours ago









    Herb WolfeHerb Wolfe

    2,3991 gold badge10 silver badges21 bronze badges




    2,3991 gold badge10 silver badges21 bronze badges










    • 1




      $begingroup$
      I added some maths formatting - hope you don't mind :-)
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
      $endgroup$
      – Rand al'Thor
      7 hours ago












    • 1




      $begingroup$
      I added some maths formatting - hope you don't mind :-)
      $endgroup$
      – Rand al'Thor
      8 hours ago










    • $begingroup$
      Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
      $endgroup$
      – Rand al'Thor
      7 hours ago







    1




    1




    $begingroup$
    I added some maths formatting - hope you don't mind :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago




    $begingroup$
    I added some maths formatting - hope you don't mind :-)
    $endgroup$
    – Rand al'Thor
    8 hours ago












    $begingroup$
    Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
    $endgroup$
    – Rand al'Thor
    7 hours ago




    $begingroup$
    Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
    $endgroup$
    – Rand al'Thor
    7 hours ago











    3














    $begingroup$

    Thanks to a comment from Ben Barden, here is another way of achieving 11 8s




    $8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$







    share|improve this answer











    $endgroup$














    • $begingroup$
      If someone got 8 8s that'd be cool.
      $endgroup$
      – Andrew
      9 hours ago










    • $begingroup$
      you could pull the same trick I did, and shave it down to 11 as well.
      $endgroup$
      – Ben Barden
      9 hours ago











    • $begingroup$
      @BenBarden Thanks, totally missed that factorisation, +1 for you.
      $endgroup$
      – hexomino
      9 hours ago










    • $begingroup$
      ...and +1 back for being the originator of my solution's ancestor.
      $endgroup$
      – Ben Barden
      9 hours ago
















    3














    $begingroup$

    Thanks to a comment from Ben Barden, here is another way of achieving 11 8s




    $8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$







    share|improve this answer











    $endgroup$














    • $begingroup$
      If someone got 8 8s that'd be cool.
      $endgroup$
      – Andrew
      9 hours ago










    • $begingroup$
      you could pull the same trick I did, and shave it down to 11 as well.
      $endgroup$
      – Ben Barden
      9 hours ago











    • $begingroup$
      @BenBarden Thanks, totally missed that factorisation, +1 for you.
      $endgroup$
      – hexomino
      9 hours ago










    • $begingroup$
      ...and +1 back for being the originator of my solution's ancestor.
      $endgroup$
      – Ben Barden
      9 hours ago














    3














    3










    3







    $begingroup$

    Thanks to a comment from Ben Barden, here is another way of achieving 11 8s




    $8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$







    share|improve this answer











    $endgroup$



    Thanks to a comment from Ben Barden, here is another way of achieving 11 8s




    $8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$








    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 9 hours ago

























    answered 9 hours ago









    hexominohexomino

    61.4k5 gold badges176 silver badges276 bronze badges




    61.4k5 gold badges176 silver badges276 bronze badges














    • $begingroup$
      If someone got 8 8s that'd be cool.
      $endgroup$
      – Andrew
      9 hours ago










    • $begingroup$
      you could pull the same trick I did, and shave it down to 11 as well.
      $endgroup$
      – Ben Barden
      9 hours ago











    • $begingroup$
      @BenBarden Thanks, totally missed that factorisation, +1 for you.
      $endgroup$
      – hexomino
      9 hours ago










    • $begingroup$
      ...and +1 back for being the originator of my solution's ancestor.
      $endgroup$
      – Ben Barden
      9 hours ago

















    • $begingroup$
      If someone got 8 8s that'd be cool.
      $endgroup$
      – Andrew
      9 hours ago










    • $begingroup$
      you could pull the same trick I did, and shave it down to 11 as well.
      $endgroup$
      – Ben Barden
      9 hours ago











    • $begingroup$
      @BenBarden Thanks, totally missed that factorisation, +1 for you.
      $endgroup$
      – hexomino
      9 hours ago










    • $begingroup$
      ...and +1 back for being the originator of my solution's ancestor.
      $endgroup$
      – Ben Barden
      9 hours ago
















    $begingroup$
    If someone got 8 8s that'd be cool.
    $endgroup$
    – Andrew
    9 hours ago




    $begingroup$
    If someone got 8 8s that'd be cool.
    $endgroup$
    – Andrew
    9 hours ago












    $begingroup$
    you could pull the same trick I did, and shave it down to 11 as well.
    $endgroup$
    – Ben Barden
    9 hours ago





    $begingroup$
    you could pull the same trick I did, and shave it down to 11 as well.
    $endgroup$
    – Ben Barden
    9 hours ago













    $begingroup$
    @BenBarden Thanks, totally missed that factorisation, +1 for you.
    $endgroup$
    – hexomino
    9 hours ago




    $begingroup$
    @BenBarden Thanks, totally missed that factorisation, +1 for you.
    $endgroup$
    – hexomino
    9 hours ago












    $begingroup$
    ...and +1 back for being the originator of my solution's ancestor.
    $endgroup$
    – Ben Barden
    9 hours ago





    $begingroup$
    ...and +1 back for being the originator of my solution's ancestor.
    $endgroup$
    – Ben Barden
    9 hours ago












    3














    $begingroup$

    Here's a solution with $9$ eights, without using the % operator:




    $$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$







    share|improve this answer









    $endgroup$



















      3














      $begingroup$

      Here's a solution with $9$ eights, without using the % operator:




      $$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$







      share|improve this answer









      $endgroup$

















        3














        3










        3







        $begingroup$

        Here's a solution with $9$ eights, without using the % operator:




        $$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$







        share|improve this answer









        $endgroup$



        Here's a solution with $9$ eights, without using the % operator:




        $$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 8 hours ago









        Jaap ScherphuisJaap Scherphuis

        19.1k1 gold badge34 silver badges83 bronze badges




        19.1k1 gold badge34 silver badges83 bronze badges
























            3














            $begingroup$

            Here is a hilarious solution for 9




            $(frac8+88)^frac888-frac8(8+8)%=1998$




            For research purposes I'll also include my kinda illegal solution for 7




            $frac8+88(frac8.8%-frac88)=1998$







            share|improve this answer









            $endgroup$














            • $begingroup$
              You won... if we include the dot. I didn't allow the dot to be used but nice work still.
              $endgroup$
              – Andrew
              6 hours ago















            3














            $begingroup$

            Here is a hilarious solution for 9




            $(frac8+88)^frac888-frac8(8+8)%=1998$




            For research purposes I'll also include my kinda illegal solution for 7




            $frac8+88(frac8.8%-frac88)=1998$







            share|improve this answer









            $endgroup$














            • $begingroup$
              You won... if we include the dot. I didn't allow the dot to be used but nice work still.
              $endgroup$
              – Andrew
              6 hours ago













            3














            3










            3







            $begingroup$

            Here is a hilarious solution for 9




            $(frac8+88)^frac888-frac8(8+8)%=1998$




            For research purposes I'll also include my kinda illegal solution for 7




            $frac8+88(frac8.8%-frac88)=1998$







            share|improve this answer









            $endgroup$



            Here is a hilarious solution for 9




            $(frac8+88)^frac888-frac8(8+8)%=1998$




            For research purposes I'll also include my kinda illegal solution for 7




            $frac8+88(frac8.8%-frac88)=1998$








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 6 hours ago









            AdamAdam

            1,0571 gold badge3 silver badges27 bronze badges




            1,0571 gold badge3 silver badges27 bronze badges














            • $begingroup$
              You won... if we include the dot. I didn't allow the dot to be used but nice work still.
              $endgroup$
              – Andrew
              6 hours ago
















            • $begingroup$
              You won... if we include the dot. I didn't allow the dot to be used but nice work still.
              $endgroup$
              – Andrew
              6 hours ago















            $begingroup$
            You won... if we include the dot. I didn't allow the dot to be used but nice work still.
            $endgroup$
            – Andrew
            6 hours ago




            $begingroup$
            You won... if we include the dot. I didn't allow the dot to be used but nice work still.
            $endgroup$
            – Andrew
            6 hours ago











            2














            $begingroup$

            Stealing gloriously from the work of others, I have it down to 11:




            $(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$







            share|improve this answer











            $endgroup$














            • $begingroup$
              I added some maths formatting - hope you don't mind :-)
              $endgroup$
              – Rand al'Thor
              8 hours ago















            2














            $begingroup$

            Stealing gloriously from the work of others, I have it down to 11:




            $(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$







            share|improve this answer











            $endgroup$














            • $begingroup$
              I added some maths formatting - hope you don't mind :-)
              $endgroup$
              – Rand al'Thor
              8 hours ago













            2














            2










            2







            $begingroup$

            Stealing gloriously from the work of others, I have it down to 11:




            $(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$







            share|improve this answer











            $endgroup$



            Stealing gloriously from the work of others, I have it down to 11:




            $(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$








            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 8 hours ago









            Rand al'Thor

            75.4k15 gold badges248 silver badges498 bronze badges




            75.4k15 gold badges248 silver badges498 bronze badges










            answered 9 hours ago









            Ben BardenBen Barden

            7861 silver badge7 bronze badges




            7861 silver badge7 bronze badges














            • $begingroup$
              I added some maths formatting - hope you don't mind :-)
              $endgroup$
              – Rand al'Thor
              8 hours ago
















            • $begingroup$
              I added some maths formatting - hope you don't mind :-)
              $endgroup$
              – Rand al'Thor
              8 hours ago















            $begingroup$
            I added some maths formatting - hope you don't mind :-)
            $endgroup$
            – Rand al'Thor
            8 hours ago




            $begingroup$
            I added some maths formatting - hope you don't mind :-)
            $endgroup$
            – Rand al'Thor
            8 hours ago











            1














            $begingroup$

            My first try, with ten:




            $frac88888 + 888 - frac88$




            Only 4 operators






            share|improve this answer








            New contributor



            Certainly not a dog is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.





            $endgroup$














            • $begingroup$
              This one is already in my answer. Nice one though!
              $endgroup$
              – Rand al'Thor
              8 hours ago










            • $begingroup$
              Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
              $endgroup$
              – Certainly not a dog
              7 hours ago










            • $begingroup$
              @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
              $endgroup$
              – Adam
              6 hours ago















            1














            $begingroup$

            My first try, with ten:




            $frac88888 + 888 - frac88$




            Only 4 operators






            share|improve this answer








            New contributor



            Certainly not a dog is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.





            $endgroup$














            • $begingroup$
              This one is already in my answer. Nice one though!
              $endgroup$
              – Rand al'Thor
              8 hours ago










            • $begingroup$
              Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
              $endgroup$
              – Certainly not a dog
              7 hours ago










            • $begingroup$
              @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
              $endgroup$
              – Adam
              6 hours ago













            1














            1










            1







            $begingroup$

            My first try, with ten:




            $frac88888 + 888 - frac88$




            Only 4 operators






            share|improve this answer








            New contributor



            Certainly not a dog is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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            $endgroup$



            My first try, with ten:




            $frac88888 + 888 - frac88$




            Only 4 operators







            share|improve this answer








            New contributor



            Certainly not a dog is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.








            share|improve this answer



            share|improve this answer






            New contributor



            Certainly not a dog is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.








            answered 8 hours ago









            Certainly not a dogCertainly not a dog

            112 bronze badges




            112 bronze badges




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            New contributor




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            • $begingroup$
              This one is already in my answer. Nice one though!
              $endgroup$
              – Rand al'Thor
              8 hours ago










            • $begingroup$
              Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
              $endgroup$
              – Certainly not a dog
              7 hours ago










            • $begingroup$
              @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
              $endgroup$
              – Adam
              6 hours ago
















            • $begingroup$
              This one is already in my answer. Nice one though!
              $endgroup$
              – Rand al'Thor
              8 hours ago










            • $begingroup$
              Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
              $endgroup$
              – Certainly not a dog
              7 hours ago










            • $begingroup$
              @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
              $endgroup$
              – Adam
              6 hours ago















            $begingroup$
            This one is already in my answer. Nice one though!
            $endgroup$
            – Rand al'Thor
            8 hours ago




            $begingroup$
            This one is already in my answer. Nice one though!
            $endgroup$
            – Rand al'Thor
            8 hours ago












            $begingroup$
            Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
            $endgroup$
            – Certainly not a dog
            7 hours ago




            $begingroup$
            Thanks! Similarly, I’ve just got another solution which I found was already posted by another user. Such is the game!
            $endgroup$
            – Certainly not a dog
            7 hours ago












            $begingroup$
            @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
            $endgroup$
            – Adam
            6 hours ago




            $begingroup$
            @Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
            $endgroup$
            – Adam
            6 hours ago











            Andrew is a new contributor. Be nice, and check out our Code of Conduct.









            draft saved

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            Andrew is a new contributor. Be nice, and check out our Code of Conduct.












            Andrew is a new contributor. Be nice, and check out our Code of Conduct.











            Andrew is a new contributor. Be nice, and check out our Code of Conduct.














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