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Squares inside a square
Block the snakeNumber wheel Challenge!Check digit number : Find the maximum number of distinct waysRook Game on a Chessboard - Take 2How many consecutive integers can you make using only four digits?What is the minimum number of digits required to make the numbers 1-20?Use 2 0 1 and 8 to make 67Use 1 9 6 2 in this order to make 75Use 0 1 2 3 4 to form 9 3-digit numbers
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Distribute the digits from 1 to 9 to a 3x3 square, such that you reach as many square numbers as possible.
A valid square number in the 3x3 square is either a single digit square number
or is build with neighbouring number(s) either vertically, horizontally or diagonally.
Example:
9 8 7
6 5 4
1 3 2
In this example the square numbers are 1, 4, 9, 16, 25, 36, 169, 961 - a total of 8 squares.
Bonus:
What is the maximum of squares in a 4x4 square, if using the hexadecimal system with digit 0-9 and A-F?
Note, square numbers here are f.e. 10=4*4 or 2A4=1A*1A.
strategy formation-of-numbers
$endgroup$
|
show 3 more comments
$begingroup$
Distribute the digits from 1 to 9 to a 3x3 square, such that you reach as many square numbers as possible.
A valid square number in the 3x3 square is either a single digit square number
or is build with neighbouring number(s) either vertically, horizontally or diagonally.
Example:
9 8 7
6 5 4
1 3 2
In this example the square numbers are 1, 4, 9, 16, 25, 36, 169, 961 - a total of 8 squares.
Bonus:
What is the maximum of squares in a 4x4 square, if using the hexadecimal system with digit 0-9 and A-F?
Note, square numbers here are f.e. 10=4*4 or 2A4=1A*1A.
strategy formation-of-numbers
$endgroup$
$begingroup$
What are the rules for 'building with neighbouring number(s)'? Would finding a line of 9-1-6 be an acceptable way to build 169 and 961, or do you have to move from one digit to the next in order without rearranging them?
$endgroup$
– Stiv
8 hours ago
1
$begingroup$
It is moving without rearranging
$endgroup$
– ThomasL
8 hours ago
$begingroup$
Got it, thanks :)
$endgroup$
– Stiv
8 hours ago
$begingroup$
Should there be a no-computers tag? I mean, do you expect the answer to be found by logic or is bruteforce coding OK?
$endgroup$
– Arnaud Mortier
7 hours ago
1
$begingroup$
The solution with 13 squares sounds good - any suggestions for the bonus question? A logical solution for thie bonus question is welcome, but brute force solution is fine as well.
$endgroup$
– ThomasL
6 hours ago
|
show 3 more comments
$begingroup$
Distribute the digits from 1 to 9 to a 3x3 square, such that you reach as many square numbers as possible.
A valid square number in the 3x3 square is either a single digit square number
or is build with neighbouring number(s) either vertically, horizontally or diagonally.
Example:
9 8 7
6 5 4
1 3 2
In this example the square numbers are 1, 4, 9, 16, 25, 36, 169, 961 - a total of 8 squares.
Bonus:
What is the maximum of squares in a 4x4 square, if using the hexadecimal system with digit 0-9 and A-F?
Note, square numbers here are f.e. 10=4*4 or 2A4=1A*1A.
strategy formation-of-numbers
$endgroup$
Distribute the digits from 1 to 9 to a 3x3 square, such that you reach as many square numbers as possible.
A valid square number in the 3x3 square is either a single digit square number
or is build with neighbouring number(s) either vertically, horizontally or diagonally.
Example:
9 8 7
6 5 4
1 3 2
In this example the square numbers are 1, 4, 9, 16, 25, 36, 169, 961 - a total of 8 squares.
Bonus:
What is the maximum of squares in a 4x4 square, if using the hexadecimal system with digit 0-9 and A-F?
Note, square numbers here are f.e. 10=4*4 or 2A4=1A*1A.
strategy formation-of-numbers
strategy formation-of-numbers
asked 9 hours ago
ThomasLThomasL
5582 silver badges19 bronze badges
5582 silver badges19 bronze badges
$begingroup$
What are the rules for 'building with neighbouring number(s)'? Would finding a line of 9-1-6 be an acceptable way to build 169 and 961, or do you have to move from one digit to the next in order without rearranging them?
$endgroup$
– Stiv
8 hours ago
1
$begingroup$
It is moving without rearranging
$endgroup$
– ThomasL
8 hours ago
$begingroup$
Got it, thanks :)
$endgroup$
– Stiv
8 hours ago
$begingroup$
Should there be a no-computers tag? I mean, do you expect the answer to be found by logic or is bruteforce coding OK?
$endgroup$
– Arnaud Mortier
7 hours ago
1
$begingroup$
The solution with 13 squares sounds good - any suggestions for the bonus question? A logical solution for thie bonus question is welcome, but brute force solution is fine as well.
$endgroup$
– ThomasL
6 hours ago
|
show 3 more comments
$begingroup$
What are the rules for 'building with neighbouring number(s)'? Would finding a line of 9-1-6 be an acceptable way to build 169 and 961, or do you have to move from one digit to the next in order without rearranging them?
$endgroup$
– Stiv
8 hours ago
1
$begingroup$
It is moving without rearranging
$endgroup$
– ThomasL
8 hours ago
$begingroup$
Got it, thanks :)
$endgroup$
– Stiv
8 hours ago
$begingroup$
Should there be a no-computers tag? I mean, do you expect the answer to be found by logic or is bruteforce coding OK?
$endgroup$
– Arnaud Mortier
7 hours ago
1
$begingroup$
The solution with 13 squares sounds good - any suggestions for the bonus question? A logical solution for thie bonus question is welcome, but brute force solution is fine as well.
$endgroup$
– ThomasL
6 hours ago
$begingroup$
What are the rules for 'building with neighbouring number(s)'? Would finding a line of 9-1-6 be an acceptable way to build 169 and 961, or do you have to move from one digit to the next in order without rearranging them?
$endgroup$
– Stiv
8 hours ago
$begingroup$
What are the rules for 'building with neighbouring number(s)'? Would finding a line of 9-1-6 be an acceptable way to build 169 and 961, or do you have to move from one digit to the next in order without rearranging them?
$endgroup$
– Stiv
8 hours ago
1
1
$begingroup$
It is moving without rearranging
$endgroup$
– ThomasL
8 hours ago
$begingroup$
It is moving without rearranging
$endgroup$
– ThomasL
8 hours ago
$begingroup$
Got it, thanks :)
$endgroup$
– Stiv
8 hours ago
$begingroup$
Got it, thanks :)
$endgroup$
– Stiv
8 hours ago
$begingroup$
Should there be a no-computers tag? I mean, do you expect the answer to be found by logic or is bruteforce coding OK?
$endgroup$
– Arnaud Mortier
7 hours ago
$begingroup$
Should there be a no-computers tag? I mean, do you expect the answer to be found by logic or is bruteforce coding OK?
$endgroup$
– Arnaud Mortier
7 hours ago
1
1
$begingroup$
The solution with 13 squares sounds good - any suggestions for the bonus question? A logical solution for thie bonus question is welcome, but brute force solution is fine as well.
$endgroup$
– ThomasL
6 hours ago
$begingroup$
The solution with 13 squares sounds good - any suggestions for the bonus question? A logical solution for thie bonus question is welcome, but brute force solution is fine as well.
$endgroup$
– ThomasL
6 hours ago
|
show 3 more comments
3 Answers
3
active
oldest
votes
$begingroup$
Best solution I could come up with was,
13 squares:
1 3 7
6 2 5
9 4 8
which includes the squares,
1, 4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
What I tried,
Mostly trying to get as much squares with 2-digit squares (only missed 81) as possible and swapping around to make 3-digit squares and prioritizing the 169-961 double 3-digit square and other 2-3-digit doubles.
I started with 169 on a column and tried making 625 and 529 on rows, and then only 4 digits are remaining and possible to intuitively add focusing on 2-digits, or even brute-force as there are only 24 possibilities.
I just tried coding this too after seeing OP's comment, and if my program was correct,
This is the maximum and only this arrangement and rotations/reflections gives the answer.
$endgroup$
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
add a comment |
$begingroup$
The best I've managed so far is
12 squares
With the following
1 8 3
7 6 4
5 2 9
which has
1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 529, 961
General Strategy
It's not too difficult to include all of the 2-digit squares. After that it's sensible to have 169 in there (as you get 961 for free) and then 529 is also easy to get in as we have 25.
$endgroup$
add a comment |
$begingroup$
Solution 1 with 2 as center
9 4 8
6 2 5
1 3 7
13 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
Strategy: I first write down the all 3 digits squares then I look for the 3 digit squares with a most solid center. means a maximum of 3 digits squares with common center number. I found there are 4 these types of squares 324, 625, 529, 729 where the common center is 2. so I made 2 is my center number and write down all the 3 digits squares. then I tried to cover the other 3 digits squares by rearranging them. then finally I look for all 2 digit squares and be able to get them mostly except 81. Also, one more thing 169 and 961 is also a good combo so don't miss it. if you see the 3 digit square list below that we can use, we can clearly see that 2 makes the most solid center so the most solid solution, after it 3 and 8 can give a better result.
Possible 3 digit squares we can use with solid centers.
324, 529, 625, 729
169, 361, 961
289, 784
841196256576
Solution 2 with 2 as center
5 7 8
3 2 4
1 6 9
same strategy 12 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 529,
961
Solution 3 with 8 as center
2 7 1
5 8 6
3 4 9
Another 12 squares 1,4, 9, 16, 25, 49, 64, 81,169, 196, 289, 784
Solution 4 as 6 as the center.
1 5 7
8 6 2
3 4 9
12 squares same strategy 1 ,4, 9, 16, 25, 49, 64, 81,169, 729, 961
New contributor
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Best solution I could come up with was,
13 squares:
1 3 7
6 2 5
9 4 8
which includes the squares,
1, 4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
What I tried,
Mostly trying to get as much squares with 2-digit squares (only missed 81) as possible and swapping around to make 3-digit squares and prioritizing the 169-961 double 3-digit square and other 2-3-digit doubles.
I started with 169 on a column and tried making 625 and 529 on rows, and then only 4 digits are remaining and possible to intuitively add focusing on 2-digits, or even brute-force as there are only 24 possibilities.
I just tried coding this too after seeing OP's comment, and if my program was correct,
This is the maximum and only this arrangement and rotations/reflections gives the answer.
$endgroup$
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
add a comment |
$begingroup$
Best solution I could come up with was,
13 squares:
1 3 7
6 2 5
9 4 8
which includes the squares,
1, 4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
What I tried,
Mostly trying to get as much squares with 2-digit squares (only missed 81) as possible and swapping around to make 3-digit squares and prioritizing the 169-961 double 3-digit square and other 2-3-digit doubles.
I started with 169 on a column and tried making 625 and 529 on rows, and then only 4 digits are remaining and possible to intuitively add focusing on 2-digits, or even brute-force as there are only 24 possibilities.
I just tried coding this too after seeing OP's comment, and if my program was correct,
This is the maximum and only this arrangement and rotations/reflections gives the answer.
$endgroup$
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
add a comment |
$begingroup$
Best solution I could come up with was,
13 squares:
1 3 7
6 2 5
9 4 8
which includes the squares,
1, 4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
What I tried,
Mostly trying to get as much squares with 2-digit squares (only missed 81) as possible and swapping around to make 3-digit squares and prioritizing the 169-961 double 3-digit square and other 2-3-digit doubles.
I started with 169 on a column and tried making 625 and 529 on rows, and then only 4 digits are remaining and possible to intuitively add focusing on 2-digits, or even brute-force as there are only 24 possibilities.
I just tried coding this too after seeing OP's comment, and if my program was correct,
This is the maximum and only this arrangement and rotations/reflections gives the answer.
$endgroup$
Best solution I could come up with was,
13 squares:
1 3 7
6 2 5
9 4 8
which includes the squares,
1, 4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
What I tried,
Mostly trying to get as much squares with 2-digit squares (only missed 81) as possible and swapping around to make 3-digit squares and prioritizing the 169-961 double 3-digit square and other 2-3-digit doubles.
I started with 169 on a column and tried making 625 and 529 on rows, and then only 4 digits are remaining and possible to intuitively add focusing on 2-digits, or even brute-force as there are only 24 possibilities.
I just tried coding this too after seeing OP's comment, and if my program was correct,
This is the maximum and only this arrangement and rotations/reflections gives the answer.
edited 6 hours ago
answered 7 hours ago
SupersonicSupersonic
1496 bronze badges
1496 bronze badges
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
add a comment |
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
$begingroup$
I coded it myself to check, you are correct that this is optimal :)
$endgroup$
– im_so_meta_even_this_acronym
5 hours ago
add a comment |
$begingroup$
The best I've managed so far is
12 squares
With the following
1 8 3
7 6 4
5 2 9
which has
1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 529, 961
General Strategy
It's not too difficult to include all of the 2-digit squares. After that it's sensible to have 169 in there (as you get 961 for free) and then 529 is also easy to get in as we have 25.
$endgroup$
add a comment |
$begingroup$
The best I've managed so far is
12 squares
With the following
1 8 3
7 6 4
5 2 9
which has
1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 529, 961
General Strategy
It's not too difficult to include all of the 2-digit squares. After that it's sensible to have 169 in there (as you get 961 for free) and then 529 is also easy to get in as we have 25.
$endgroup$
add a comment |
$begingroup$
The best I've managed so far is
12 squares
With the following
1 8 3
7 6 4
5 2 9
which has
1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 529, 961
General Strategy
It's not too difficult to include all of the 2-digit squares. After that it's sensible to have 169 in there (as you get 961 for free) and then 529 is also easy to get in as we have 25.
$endgroup$
The best I've managed so far is
12 squares
With the following
1 8 3
7 6 4
5 2 9
which has
1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 529, 961
General Strategy
It's not too difficult to include all of the 2-digit squares. After that it's sensible to have 169 in there (as you get 961 for free) and then 529 is also easy to get in as we have 25.
answered 7 hours ago
hexominohexomino
60.4k5 gold badges174 silver badges274 bronze badges
60.4k5 gold badges174 silver badges274 bronze badges
add a comment |
add a comment |
$begingroup$
Solution 1 with 2 as center
9 4 8
6 2 5
1 3 7
13 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
Strategy: I first write down the all 3 digits squares then I look for the 3 digit squares with a most solid center. means a maximum of 3 digits squares with common center number. I found there are 4 these types of squares 324, 625, 529, 729 where the common center is 2. so I made 2 is my center number and write down all the 3 digits squares. then I tried to cover the other 3 digits squares by rearranging them. then finally I look for all 2 digit squares and be able to get them mostly except 81. Also, one more thing 169 and 961 is also a good combo so don't miss it. if you see the 3 digit square list below that we can use, we can clearly see that 2 makes the most solid center so the most solid solution, after it 3 and 8 can give a better result.
Possible 3 digit squares we can use with solid centers.
324, 529, 625, 729
169, 361, 961
289, 784
841196256576
Solution 2 with 2 as center
5 7 8
3 2 4
1 6 9
same strategy 12 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 529,
961
Solution 3 with 8 as center
2 7 1
5 8 6
3 4 9
Another 12 squares 1,4, 9, 16, 25, 49, 64, 81,169, 196, 289, 784
Solution 4 as 6 as the center.
1 5 7
8 6 2
3 4 9
12 squares same strategy 1 ,4, 9, 16, 25, 49, 64, 81,169, 729, 961
New contributor
$endgroup$
add a comment |
$begingroup$
Solution 1 with 2 as center
9 4 8
6 2 5
1 3 7
13 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
Strategy: I first write down the all 3 digits squares then I look for the 3 digit squares with a most solid center. means a maximum of 3 digits squares with common center number. I found there are 4 these types of squares 324, 625, 529, 729 where the common center is 2. so I made 2 is my center number and write down all the 3 digits squares. then I tried to cover the other 3 digits squares by rearranging them. then finally I look for all 2 digit squares and be able to get them mostly except 81. Also, one more thing 169 and 961 is also a good combo so don't miss it. if you see the 3 digit square list below that we can use, we can clearly see that 2 makes the most solid center so the most solid solution, after it 3 and 8 can give a better result.
Possible 3 digit squares we can use with solid centers.
324, 529, 625, 729
169, 361, 961
289, 784
841196256576
Solution 2 with 2 as center
5 7 8
3 2 4
1 6 9
same strategy 12 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 529,
961
Solution 3 with 8 as center
2 7 1
5 8 6
3 4 9
Another 12 squares 1,4, 9, 16, 25, 49, 64, 81,169, 196, 289, 784
Solution 4 as 6 as the center.
1 5 7
8 6 2
3 4 9
12 squares same strategy 1 ,4, 9, 16, 25, 49, 64, 81,169, 729, 961
New contributor
$endgroup$
add a comment |
$begingroup$
Solution 1 with 2 as center
9 4 8
6 2 5
1 3 7
13 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
Strategy: I first write down the all 3 digits squares then I look for the 3 digit squares with a most solid center. means a maximum of 3 digits squares with common center number. I found there are 4 these types of squares 324, 625, 529, 729 where the common center is 2. so I made 2 is my center number and write down all the 3 digits squares. then I tried to cover the other 3 digits squares by rearranging them. then finally I look for all 2 digit squares and be able to get them mostly except 81. Also, one more thing 169 and 961 is also a good combo so don't miss it. if you see the 3 digit square list below that we can use, we can clearly see that 2 makes the most solid center so the most solid solution, after it 3 and 8 can give a better result.
Possible 3 digit squares we can use with solid centers.
324, 529, 625, 729
169, 361, 961
289, 784
841196256576
Solution 2 with 2 as center
5 7 8
3 2 4
1 6 9
same strategy 12 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 529,
961
Solution 3 with 8 as center
2 7 1
5 8 6
3 4 9
Another 12 squares 1,4, 9, 16, 25, 49, 64, 81,169, 196, 289, 784
Solution 4 as 6 as the center.
1 5 7
8 6 2
3 4 9
12 squares same strategy 1 ,4, 9, 16, 25, 49, 64, 81,169, 729, 961
New contributor
$endgroup$
Solution 1 with 2 as center
9 4 8
6 2 5
1 3 7
13 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 625, 729, 961
Strategy: I first write down the all 3 digits squares then I look for the 3 digit squares with a most solid center. means a maximum of 3 digits squares with common center number. I found there are 4 these types of squares 324, 625, 529, 729 where the common center is 2. so I made 2 is my center number and write down all the 3 digits squares. then I tried to cover the other 3 digits squares by rearranging them. then finally I look for all 2 digit squares and be able to get them mostly except 81. Also, one more thing 169 and 961 is also a good combo so don't miss it. if you see the 3 digit square list below that we can use, we can clearly see that 2 makes the most solid center so the most solid solution, after it 3 and 8 can give a better result.
Possible 3 digit squares we can use with solid centers.
324, 529, 625, 729
169, 361, 961
289, 784
841196256576
Solution 2 with 2 as center
5 7 8
3 2 4
1 6 9
same strategy 12 squares 1,4, 9, 16, 25, 36, 49, 64, 169, 324, 529,
961
Solution 3 with 8 as center
2 7 1
5 8 6
3 4 9
Another 12 squares 1,4, 9, 16, 25, 49, 64, 81,169, 196, 289, 784
Solution 4 as 6 as the center.
1 5 7
8 6 2
3 4 9
12 squares same strategy 1 ,4, 9, 16, 25, 49, 64, 81,169, 729, 961
New contributor
edited 4 hours ago
New contributor
answered 5 hours ago
Sayed Mohd AliSayed Mohd Ali
19113 bronze badges
19113 bronze badges
New contributor
New contributor
add a comment |
add a comment |
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$begingroup$
What are the rules for 'building with neighbouring number(s)'? Would finding a line of 9-1-6 be an acceptable way to build 169 and 961, or do you have to move from one digit to the next in order without rearranging them?
$endgroup$
– Stiv
8 hours ago
1
$begingroup$
It is moving without rearranging
$endgroup$
– ThomasL
8 hours ago
$begingroup$
Got it, thanks :)
$endgroup$
– Stiv
8 hours ago
$begingroup$
Should there be a no-computers tag? I mean, do you expect the answer to be found by logic or is bruteforce coding OK?
$endgroup$
– Arnaud Mortier
7 hours ago
1
$begingroup$
The solution with 13 squares sounds good - any suggestions for the bonus question? A logical solution for thie bonus question is welcome, but brute force solution is fine as well.
$endgroup$
– ThomasL
6 hours ago