Complete the Square Grid!

Logic Level 2

In the diagram given above, the numbers from 1 to 25 are to arranged in a $5 \times 5$ square grid so that each number except 1 and 2, is the sum of two of its neighbours . Some of the numbers have already been filled in. Which number must replace the " $?$ " when the grid is complete.

Note - Numbers in the grid are neighbours if their squares touch along a side or at a corner. For example: the number "1" has eight neighbours , the number "21" has three neighbours .

Bonus - Complete the Grid.

14 15 18 11 10 19 12 13

2 solutions

Janardhanan Sivaramakrishnan
Aug 20, 2015

The solved grid would be

19	11	15	20	21
13	6	5	4	17
23	7	1	3	14
16	9	8	2	12
25	24	18	10	22

11 and 18 can be interchanged, fyi

Sarvesh Nalawade - 5 years, 3 months ago

Yeah, I did it and got 18 as well.

Bobby Lawrence - 5 years, 3 months ago

If youswap 18 and 11, how do you get the 15?

alex sobel - 5 years, 2 months ago

No. There's only one way to fill in the numbers, and it's the way that Janardhanan Sivaramakrishnan said.

Peter Byers - 5 years ago

yeah, my mistake

Sarvesh Nalawade - 5 years ago

To get 15 you need the 11 to be up there (11 + 4 = 15)

anjaly jeyacanthan - 1 year, 1 month ago

There is no sum for 15 or 24 in this solution. Everything else adds up. The problem is frustrating because it doesn't seem like this grid setup can be completed. 14 works for the actual question but a fully filled grid is fallacious based on the rules and setup.

Justin Marshall - 4 years, 11 months ago

15 is the sum of 11 and 4. And 24 is the sum of 16 and 8. It works?

Jon Danford - 4 years, 8 months ago

You should add that you can't repeat a number, because if you could there are other ways to solve it. (I think ...) Anyway, it's a good problem :)

Gerard Calvo Bartra - 5 years ago

Kobi Shiran
Aug 18, 2015

Start from right up corner.

21 must be sum of 20,4, and x.(2 of them)

It cannot be 20+4 because it is too big and not 20+x, since x cannot be 1 (it is written). So 21 must be 4+x such means x=17.

Now right bottom corner. 22 must be sum of 2,x and b.(2 of them)

It cannot be 2+20 (a/b=20) since 20 is already written. So it must be the sum of a+b. We know 1-9 is written so it must be 10 and 12. (can't be double 11 or 1-9). So the number in square over 22 must be 10 or 12. Now look at 17. It must be sum of 21,20,4,3 and ?. It cannot be sum of 21/20 with anything so we have options 3,4 and ?. Means ? Can be 14 or 13.

Now if we look back at the square over 22 we can see that 10 can not be summed by his surroundings (22,12,2,3,13/14).

So the square over 22 must be 12. (which summed by 10,2).

So ? must be 14 since it is surrounded by 12,2,3,4,17 and we know it must be 13/14. 13 is not option since we cannot make it by the surroundings so

14 is the right aswwer. (12+2).

That's how I did it too.

Peter Byers - 5 years ago

Complete the Square Grid!

2 solutions

0 pending reports