9sums - a logical deduction puzzle
up vote
6
down vote
favorite
Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.
--- --- --- ---
13 14 11
--- --- --- ---
11 10 13
--- --- --- ---
11 9 14
--- --- --- ---
Can you solve the grid?
mathematics logical-deduction calculation-puzzle
asked Dec 11 at 8:57
JonMark Perry
17k63281
add a comment |
up vote
6
down vote
favorite
Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.
--- --- --- ---
13 14 11
--- --- --- ---
11 10 13
--- --- --- ---
11 9 14
--- --- --- ---
Can you solve the grid?
mathematics logical-deduction calculation-puzzle
asked Dec 11 at 8:57
JonMark Perry
17k63281
Are there any rules on number of uses of each integer or using the same integer per row/column?
– AHKieran
Dec 11 at 9:04
@AHKieran; not yet!
– JonMark Perry
Dec 11 at 9:07
add a comment |
up vote
6
down vote
favorite
up vote
6
down vote
favorite
Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.
--- --- --- ---
13 14 11
--- --- --- ---
11 10 13
--- --- --- ---
11 9 14
--- --- --- ---
Can you solve the grid?
mathematics logical-deduction calculation-puzzle
asked Dec 11 at 8:57
JonMark Perry
17k63281
Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.
--- --- --- ---
13 14 11
--- --- --- ---
11 10 13
--- --- --- ---
11 9 14
--- --- --- ---
Can you solve the grid?
mathematics logical-deduction calculation-puzzle
mathematics logical-deduction calculation-puzzle
asked Dec 11 at 8:57
JonMark Perry
17k63281
asked Dec 11 at 8:57
JonMark Perry
17k63281
asked Dec 11 at 8:57
JonMark Perry
17k63281
asked Dec 11 at 8:57
JonMark Perry
17k63281
asked Dec 11 at 8:57
JonMark Perry
17k63281
17k63281
Are there any rules on number of uses of each integer or using the same integer per row/column?
– AHKieran
Dec 11 at 9:04
@AHKieran; not yet!
– JonMark Perry
Dec 11 at 9:07
add a comment |
Are there any rules on number of uses of each integer or using the same integer per row/column?
– AHKieran
Dec 11 at 9:04
@AHKieran; not yet!
– JonMark Perry
Dec 11 at 9:07
Are there any rules on number of uses of each integer or using the same integer per row/column?
– AHKieran
Dec 11 at 9:04
Are there any rules on number of uses of each integer or using the same integer per row/column?
– AHKieran
Dec 11 at 9:04
@AHKieran; not yet!
– JonMark Perry
Dec 11 at 9:07
@AHKieran; not yet!
– JonMark Perry
Dec 11 at 9:07
add a comment |
7 Answers
7
active
oldest
votes
up vote
7
down vote
accepted
2 5 3 1
13 14 11
3 3 3 4
11 10 13
4 1 3 3
11 9 14
5 1 4 4
edited Dec 11 at 9:19
Christoph
3,3961426
answered Dec 11 at 9:07
Alex
963
1
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
add a comment |
up vote
3
down vote
My answer:
Not sure how to format this, but from left to right, then top to bottom, the numbers would be:
2, 5, 5, 1
5, 1, 3, 2
2, 3, 3, 5
5, 1, 2, 4
answered Dec 11 at 9:20
AHKieran
4,176737
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
add a comment |
up vote
3
down vote
Its has many solutons, just need to start somewhere
3 3 3 1
13 14 11
2 5 3 4
11 10 13
2 1 1 5
11 9 14
5 3 4 4
answered Dec 11 at 9:21
Naeem Shaikh
829410
add a comment |
up vote
3
down vote
Here is my solution in excel:
If you want to solve it by yourself, here is file 9sum.xlsx.
edited yesterday
S. M.
837413
answered Dec 11 at 10:44
cluster_master
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
3
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
add a comment |
up vote
2
down vote
Also this grid is a solution :
2 4 5 2
3 4 1 3
3 1 4 5
4 3 1 4
edited Dec 11 at 10:11
u_ndefined
2,638436
answered Dec 11 at 9:53
richard
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup>!.
– u_ndefined
Dec 11 at 10:14
add a comment |
up vote
1
down vote
This was fun!
For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.
-3- -4- -4- -1-
13 14 11
-1- -5- -1- -5-
11 10 13
-3- -2- -2- -5-
11 9 14
-5- -1- -4- -3-
answered Dec 11 at 12:10
Marv
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
2 5 3 2
13 14 11
3 3 3 3
11 10 13
3 2 2 5
11 9 14
4 2 3 4
Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)
answered 23 hours ago
kwypston
1763
add a comment |
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7 Answers
7
active
oldest
votes
7 Answers
7
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
accepted
2 5 3 1
13 14 11
3 3 3 4
11 10 13
4 1 3 3
11 9 14
5 1 4 4
edited Dec 11 at 9:19
Christoph
3,3961426
answered Dec 11 at 9:07
Alex
963
1
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
add a comment |
up vote
7
down vote
accepted
2 5 3 1
13 14 11
3 3 3 4
11 10 13
4 1 3 3
11 9 14
5 1 4 4
edited Dec 11 at 9:19
Christoph
3,3961426
answered Dec 11 at 9:07
Alex
963
1
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
add a comment |
up vote
7
down vote
accepted
up vote
7
down vote
accepted
2 5 3 1
13 14 11
3 3 3 4
11 10 13
4 1 3 3
11 9 14
5 1 4 4
edited Dec 11 at 9:19
Christoph
3,3961426
answered Dec 11 at 9:07
Alex
963
2 5 3 1
13 14 11
3 3 3 4
11 10 13
4 1 3 3
11 9 14
5 1 4 4
edited Dec 11 at 9:19
Christoph
3,3961426
answered Dec 11 at 9:07
Alex
963
edited Dec 11 at 9:19
Christoph
3,3961426
edited Dec 11 at 9:19
Christoph
3,3961426
edited Dec 11 at 9:19
Christoph
3,3961426
3,3961426
answered Dec 11 at 9:07
Alex
963
answered Dec 11 at 9:07
Alex
963
answered Dec 11 at 9:07
Alex
963
963
1
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
add a comment |
1
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
1
1
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
Well done! I edited the answer to make it a little more readable.
– Christoph
Dec 11 at 9:20
add a comment |
up vote
3
down vote
My answer:
Not sure how to format this, but from left to right, then top to bottom, the numbers would be:
2, 5, 5, 1
5, 1, 3, 2
2, 3, 3, 5
5, 1, 2, 4
answered Dec 11 at 9:20
AHKieran
4,176737
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
add a comment |
up vote
3
down vote
My answer:
Not sure how to format this, but from left to right, then top to bottom, the numbers would be:
2, 5, 5, 1
5, 1, 3, 2
2, 3, 3, 5
5, 1, 2, 4
answered Dec 11 at 9:20
AHKieran
4,176737
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
add a comment |
up vote
3
down vote
up vote
3
down vote
My answer:
Not sure how to format this, but from left to right, then top to bottom, the numbers would be:
2, 5, 5, 1
5, 1, 3, 2
2, 3, 3, 5
5, 1, 2, 4
answered Dec 11 at 9:20
AHKieran
4,176737
My answer:
Not sure how to format this, but from left to right, then top to bottom, the numbers would be:
2, 5, 5, 1
5, 1, 3, 2
2, 3, 3, 5
5, 1, 2, 4
answered Dec 11 at 9:20
AHKieran
4,176737
answered Dec 11 at 9:20
AHKieran
4,176737
answered Dec 11 at 9:20
AHKieran
4,176737
answered Dec 11 at 9:20
AHKieran
4,176737
4,176737
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
add a comment |
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
– AHKieran
Dec 11 at 9:21
add a comment |
up vote
3
down vote
Its has many solutons, just need to start somewhere
3 3 3 1
13 14 11
2 5 3 4
11 10 13
2 1 1 5
11 9 14
5 3 4 4
answered Dec 11 at 9:21
Naeem Shaikh
829410
add a comment |
up vote
3
down vote
Its has many solutons, just need to start somewhere
3 3 3 1
13 14 11
2 5 3 4
11 10 13
2 1 1 5
11 9 14
5 3 4 4
answered Dec 11 at 9:21
Naeem Shaikh
829410
add a comment |
up vote
3
down vote
up vote
3
down vote
Its has many solutons, just need to start somewhere
3 3 3 1
13 14 11
2 5 3 4
11 10 13
2 1 1 5
11 9 14
5 3 4 4
answered Dec 11 at 9:21
Naeem Shaikh
829410
Its has many solutons, just need to start somewhere
3 3 3 1
13 14 11
2 5 3 4
11 10 13
2 1 1 5
11 9 14
5 3 4 4
answered Dec 11 at 9:21
Naeem Shaikh
829410
answered Dec 11 at 9:21
Naeem Shaikh
829410
answered Dec 11 at 9:21
Naeem Shaikh
829410
answered Dec 11 at 9:21
Naeem Shaikh
829410
829410
add a comment |
add a comment |
up vote
3
down vote
Here is my solution in excel:
If you want to solve it by yourself, here is file 9sum.xlsx.
edited yesterday
S. M.
837413
answered Dec 11 at 10:44
cluster_master
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
3
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
add a comment |
up vote
3
down vote
Here is my solution in excel:
If you want to solve it by yourself, here is file 9sum.xlsx.
edited yesterday
S. M.
837413
answered Dec 11 at 10:44
cluster_master
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
3
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
add a comment |
up vote
3
down vote
up vote
3
down vote
Here is my solution in excel:
If you want to solve it by yourself, here is file 9sum.xlsx.
edited yesterday
S. M.
837413
answered Dec 11 at 10:44
cluster_master
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Here is my solution in excel:
If you want to solve it by yourself, here is file 9sum.xlsx.
edited yesterday
S. M.
837413
answered Dec 11 at 10:44
cluster_master
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
S. M.
837413
edited yesterday
S. M.
837413
edited yesterday
S. M.
837413
837413
answered Dec 11 at 10:44
cluster_master
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Dec 11 at 10:44
cluster_master
313
answered Dec 11 at 10:44
cluster_master
313
313
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
cluster_master is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
3
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
add a comment |
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
3
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
– Christoph
Dec 11 at 11:24
3
3
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
What you could do is take a screenshot of your excel and upload it as an answer
– AHKieran
Dec 11 at 11:25
add a comment |
up vote
2
down vote
Also this grid is a solution :
2 4 5 2
3 4 1 3
3 1 4 5
4 3 1 4
edited Dec 11 at 10:11
u_ndefined
2,638436
answered Dec 11 at 9:53
richard
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup>!.
– u_ndefined
Dec 11 at 10:14
add a comment |
up vote
2
down vote
Also this grid is a solution :
2 4 5 2
3 4 1 3
3 1 4 5
4 3 1 4
edited Dec 11 at 10:11
u_ndefined
2,638436
answered Dec 11 at 9:53
richard
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup>!.
– u_ndefined
Dec 11 at 10:14
add a comment |
up vote
2
down vote
up vote
2
down vote
Also this grid is a solution :
2 4 5 2
3 4 1 3
3 1 4 5
4 3 1 4
edited Dec 11 at 10:11
u_ndefined
2,638436
answered Dec 11 at 9:53
richard
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Also this grid is a solution :
2 4 5 2
3 4 1 3
3 1 4 5
4 3 1 4
edited Dec 11 at 10:11
u_ndefined
2,638436
answered Dec 11 at 9:53
richard
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Dec 11 at 10:11
u_ndefined
2,638436
edited Dec 11 at 10:11
u_ndefined
2,638436
edited Dec 11 at 10:11
u_ndefined
2,638436
2,638436
answered Dec 11 at 9:53
richard
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Dec 11 at 9:53
richard
211
answered Dec 11 at 9:53
richard
211
211
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
richard is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup>!.
– u_ndefined
Dec 11 at 10:14
add a comment |
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup>!.
– u_ndefined
Dec 11 at 10:14
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup
>!.– u_ndefined
Dec 11 at 10:14
Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup
>!.– u_ndefined
Dec 11 at 10:14
add a comment |
up vote
1
down vote
This was fun!
For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.
-3- -4- -4- -1-
13 14 11
-1- -5- -1- -5-
11 10 13
-3- -2- -2- -5-
11 9 14
-5- -1- -4- -3-
answered Dec 11 at 12:10
Marv
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
1
down vote
This was fun!
For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.
-3- -4- -4- -1-
13 14 11
-1- -5- -1- -5-
11 10 13
-3- -2- -2- -5-
11 9 14
-5- -1- -4- -3-
answered Dec 11 at 12:10
Marv
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
1
down vote
up vote
1
down vote
This was fun!
For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.
-3- -4- -4- -1-
13 14 11
-1- -5- -1- -5-
11 10 13
-3- -2- -2- -5-
11 9 14
-5- -1- -4- -3-
answered Dec 11 at 12:10
Marv
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
This was fun!
For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.
-3- -4- -4- -1-
13 14 11
-1- -5- -1- -5-
11 10 13
-3- -2- -2- -5-
11 9 14
-5- -1- -4- -3-
answered Dec 11 at 12:10
Marv
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Dec 11 at 12:10
Marv
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Dec 11 at 12:10
Marv
1134
answered Dec 11 at 12:10
Marv
1134
1134
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Marv is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
up vote
0
down vote
2 5 3 2
13 14 11
3 3 3 3
11 10 13
3 2 2 5
11 9 14
4 2 3 4
Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)
answered 23 hours ago
kwypston
1763
add a comment |
up vote
0
down vote
2 5 3 2
13 14 11
3 3 3 3
11 10 13
3 2 2 5
11 9 14
4 2 3 4
Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)
answered 23 hours ago
kwypston
1763
add a comment |
up vote
0
down vote
up vote
0
down vote
2 5 3 2
13 14 11
3 3 3 3
11 10 13
3 2 2 5
11 9 14
4 2 3 4
Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)
answered 23 hours ago
kwypston
1763
2 5 3 2
13 14 11
3 3 3 3
11 10 13
3 2 2 5
11 9 14
4 2 3 4
Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)
answered 23 hours ago
kwypston
1763
answered 23 hours ago
kwypston
1763
answered 23 hours ago
kwypston
1763
answered 23 hours ago
kwypston
1763
1763
add a comment |
add a comment |
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Are there any rules on number of uses of each integer or using the same integer per row/column?
– AHKieran
Dec 11 at 9:04
@AHKieran; not yet!
– JonMark Perry
Dec 11 at 9:07