superprismatic Posted July 27, 2009 Report Share Posted July 27, 2009 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? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 27, 2009 Author Report Share Posted July 27, 2009 Sorry! You don't have 23 as one of the coordinates. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 I believe in the original problem statement you mean that "23" is one of the axis coordinates? Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 27, 2009 Author Report Share Posted July 27, 2009 I believe in the original problem statement you mean that "23" is one of the axis coordinates? Yes. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 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? Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 27, 2009 Author Report Share Posted July 27, 2009 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? What I mean by "coordinates" are the numbers either written down the side of the grid or across the top of it. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 27, 2009 Author Report Share Posted July 27, 2009 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 do the coordinates all have to be different? Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 27, 2009 Author Report Share Posted July 27, 2009 do the coordinates all have to be different? No. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 (edited) table.bmp Edited July 27, 2009 by nuclearlemons Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 table.bmp 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 1 2 3 4 5 6 7 8 0 8 16 24 32 40 48 56 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 27, 2009 Report Share Posted July 27, 2009 oooops! I just looked at the other answers and saw my error - I didn't use 23.....back to the drawing board.... Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 28, 2009 Author Report Share Posted July 28, 2009 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. 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 28, 2009 Report Share Posted July 28, 2009 Here is the one for a 16 by 16 grid. Anyone notice a pattern???? sixteen.bmp Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted July 28, 2009 Author Report Share Posted July 28, 2009 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...... Quote Link to comment Share on other sites More sharing options...
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superprismatic
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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