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One set of eight positive integers is written down the

side of an 8x8 square grid, another set of eight across

the top. The entry in any cell of the grid is the sum

of the corresponding side and top coordinates. These

entries are the numbers from 1 to 64 inclusive. If

one of the coordinates is 23, what are the others?

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Sorry! You don't have 23 as one of the coordinates.

What do you mean he dont have 23 as one of the co-ordinates? It is present in 4th row. Do you mean u need it at the starting position?

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One set of eight positive integers is written down the

side of an 8x8 square grid, another set of eight across

the top. The entry in any cell of the grid is the sum

of the corresponding side and top coordinates. These

entries are the numbers from 1 to 64 inclusive. If

one of the coordinates is 23, what are the others?

CORRECTION ON THE PROBLEM STATEMENT:

"positive integers" in the problem should be "non-negative integers".

Sorry, I copied this verbatim from my source (privately published

material) and I didn't notice that the problem can't be solved

without 0 as one of the coordinates.

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Yeah that's exactly what I got.

Why do I waste my time doing these when someone already comes up with the answer just before I post. :duh:

Yeah, nuclearlemons got it right. But, It's such a well designed puzzle that it's a pleasure to work it out!

I'd still like to see a really elegant way to solve it. My method was very brute force. In particular,

I'd be interested in a simple algorithm which would be easy to program. My method is very messy. Why don't

you try the analogous puzzle for a 10x10 having entries from 1 to 100 also with a coordinate of 23? Give me

some direction on how you solved it.

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Here is the one for a 16 by 16 grid.

Anyone notice a pattern???? :)

sixteen.bmp

Your post made me think. Forgetting about the 23 business, what is the number of ways to make coordinates which give you all n^2 values in a n by n grid? One set of coordinates should be increasing starting at 0 and the other set increasing starting at 1. Do you have any idea? For a 2 by 2 there are 2 ways: (0,1)(1,3) and (0,2)(1,2). For a 3 by 3 there are also 2 ways: (0,1,2)(1,4,7) and (0,3,6)(1,2,3). For 4 by 4 there are 6 ways......

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