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;
$begingroup$
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.
formation-of-numbers
New contributor
$endgroup$
|
show 1 more comment
$begingroup$
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.
formation-of-numbers
New contributor
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
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.
formation-of-numbers
New contributor
$endgroup$
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
formation-of-numbers
New contributor
New contributor
edited 8 hours ago
Andrew
New contributor
asked 9 hours ago
AndrewAndrew
1414 bronze badges
1414 bronze badges
New contributor
New contributor
$begingroup$
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
|
show 1 more comment
$begingroup$
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
|
show 1 more comment
8 Answers
8
active
oldest
votes
$begingroup$
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:
$$8 times (8+8) times (8+8) - frac88%+8% $$
$$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
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):
$$frac88888 + 888 - frac88$$
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
I have a solution with 12 8s
$((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$
Updated, another with 9 8s
$frac8888-88 + 888$
$endgroup$
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
add a comment
|
$begingroup$
Thanks to a comment from Ben Barden, here is another way of achieving 11 8s
$8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$
$endgroup$
$begingroup$
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
add a comment
|
$begingroup$
Here's a solution with $9$ eights, without using the % operator:
$$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$
$endgroup$
add a comment
|
$begingroup$
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
$frac8+88(frac8.8%-frac88)=1998$
$endgroup$
$begingroup$
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
add a comment
|
$begingroup$
Stealing gloriously from the work of others, I have it down to 11:
$(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$
$endgroup$
$begingroup$
I added some maths formatting - hope you don't mind :-)
$endgroup$
– Rand al'Thor
8 hours ago
add a comment
|
$begingroup$
My first try, with ten:
$frac88888 + 888 - frac88$
Only 4 operators
New contributor
$endgroup$
$begingroup$
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
add a comment
|
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8 Answers
8
active
oldest
votes
8 Answers
8
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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:
$$8 times (8+8) times (8+8) - frac88%+8% $$
$$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
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:
$$8 times (8+8) times (8+8) - frac88%+8% $$
$$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
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:
$$8 times (8+8) times (8+8) - frac88%+8% $$
$$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$
$endgroup$
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:
$$8 times (8+8) times (8+8) - frac88%+8% $$
$$ = 8times16times16 - frac8.16 = 2048 - 50 = 1998 $$
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
|
show 1 more comment
$begingroup$
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
|
show 1 more comment
$begingroup$
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):
$$frac88888 + 888 - frac88$$
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
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):
$$frac88888 + 888 - frac88$$
$endgroup$
$begingroup$
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
|
show 1 more comment
$begingroup$
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):
$$frac88888 + 888 - frac88$$
$endgroup$
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):
$$frac88888 + 888 - frac88$$
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
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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!
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– Andrew
8 hours ago
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Wow! I was expecting this to be still not optimal, since in a previous comment you mentioned eight 8s.
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– Rand al'Thor
8 hours ago
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@Andrew By the way, please could you edit the source into the question? People may vote to close it otherwise.
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– Rand al'Thor
8 hours ago
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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.
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– Andrew
8 hours ago
1
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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.
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– Ben Barden
7 hours ago
|
show 1 more comment
$begingroup$
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
|
show 1 more comment
$begingroup$
I have a solution with 12 8s
$((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$
Updated, another with 9 8s
$frac8888-88 + 888$
$endgroup$
1
$begingroup$
I added some maths formatting - hope you don't mind :-)
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– Rand al'Thor
8 hours ago
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Ooh, nice: your nine-8 solution is a polished version of my ten-8 one.
$endgroup$
– Rand al'Thor
7 hours ago
add a comment
|
$begingroup$
I have a solution with 12 8s
$((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$
Updated, another with 9 8s
$frac8888-88 + 888$
$endgroup$
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
add a comment
|
$begingroup$
I have a solution with 12 8s
$((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$
Updated, another with 9 8s
$frac8888-88 + 888$
$endgroup$
I have a solution with 12 8s
$((8+8) times (8+8) times 8) - (8times8) + (8+8) - frac8+88$
Updated, another with 9 8s
$frac8888-88 + 888$
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
add a comment
|
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
add a comment
|
$begingroup$
Thanks to a comment from Ben Barden, here is another way of achieving 11 8s
$8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$
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If someone got 8 8s that'd be cool.
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– Andrew
9 hours ago
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you could pull the same trick I did, and shave it down to 11 as well.
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– Ben Barden
9 hours ago
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@BenBarden Thanks, totally missed that factorisation, +1 for you.
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– hexomino
9 hours ago
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...and +1 back for being the originator of my solution's ancestor.
$endgroup$
– Ben Barden
9 hours ago
add a comment
|
$begingroup$
Thanks to a comment from Ben Barden, here is another way of achieving 11 8s
$8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$
$endgroup$
$begingroup$
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
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@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
add a comment
|
$begingroup$
Thanks to a comment from Ben Barden, here is another way of achieving 11 8s
$8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$
$endgroup$
Thanks to a comment from Ben Barden, here is another way of achieving 11 8s
$8+8+left(left(frac8+88right)^8 - 8right)times 8-frac8+88$
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
add a comment
|
$begingroup$
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
add a comment
|
$begingroup$
Here's a solution with $9$ eights, without using the % operator:
$$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$
$endgroup$
add a comment
|
$begingroup$
Here's a solution with $9$ eights, without using the % operator:
$$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$
$endgroup$
add a comment
|
$begingroup$
Here's a solution with $9$ eights, without using the % operator:
$$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$
$endgroup$
Here's a solution with $9$ eights, without using the % operator:
$$ frac8888 ( 8+8 + frac8+88) = 111*18=1998$$
answered 8 hours ago
Jaap ScherphuisJaap Scherphuis
19.1k1 gold badge34 silver badges83 bronze badges
19.1k1 gold badge34 silver badges83 bronze badges
add a comment
|
add a comment
|
$begingroup$
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
$frac8+88(frac8.8%-frac88)=1998$
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$begingroup$
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
add a comment
|
$begingroup$
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
$frac8+88(frac8.8%-frac88)=1998$
$endgroup$
$begingroup$
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
add a comment
|
$begingroup$
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
$frac8+88(frac8.8%-frac88)=1998$
$endgroup$
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
$frac8+88(frac8.8%-frac88)=1998$
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
add a comment
|
$begingroup$
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
add a comment
|
$begingroup$
Stealing gloriously from the work of others, I have it down to 11:
$(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$
$endgroup$
$begingroup$
I added some maths formatting - hope you don't mind :-)
$endgroup$
– Rand al'Thor
8 hours ago
add a comment
|
$begingroup$
Stealing gloriously from the work of others, I have it down to 11:
$(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$
$endgroup$
$begingroup$
I added some maths formatting - hope you don't mind :-)
$endgroup$
– Rand al'Thor
8 hours ago
add a comment
|
$begingroup$
Stealing gloriously from the work of others, I have it down to 11:
$(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$
$endgroup$
Stealing gloriously from the work of others, I have it down to 11:
$(((8+8) times (8+8) - 8) times 8) + (8+8) - frac8+88$
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
add a comment
|
$begingroup$
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
add a comment
|
$begingroup$
My first try, with ten:
$frac88888 + 888 - frac88$
Only 4 operators
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
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@Brandon_J what makes you say that? I see no connection to Rubio whatsoever!
$endgroup$
– Adam
6 hours ago
add a comment
|
$begingroup$
My first try, with ten:
$frac88888 + 888 - frac88$
Only 4 operators
New contributor
$endgroup$
$begingroup$
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
add a comment
|
$begingroup$
My first try, with ten:
$frac88888 + 888 - frac88$
Only 4 operators
New contributor
$endgroup$
My first try, with ten:
$frac88888 + 888 - frac88$
Only 4 operators
New contributor
New contributor
answered 8 hours ago
Certainly not a dogCertainly not a dog
112 bronze badges
112 bronze badges
New contributor
New contributor
$begingroup$
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
add a comment
|
$begingroup$
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
add a comment
|
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.
Andrew is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
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