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Topic: integer grid (Read 3352 times) 

antkor
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Posts: 30


integer grid
« on: Nov 29^{th}, 2013, 10:05am » 
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Make a grid consisting of 6 columns and 6 rows. In each one of the 36 cells that are formed, you must place a positive integer. Each positive integer must have all smaller positive integers in one of its' neighboring cells. For example, if you choose to place the number 3 inside a cell, then each numbers 1 and 2 must be in a cell that is up, down, left or right from 3 (the remaining two cells may contain any integers as long as these integers obey to the rules as well. diagonal cells do not count as neighboring cells.). When you place all the 36 numbers inside, their sum must be exactly 93. Can you do it? (additional comment: 0 does not count as a positive integer, so you cannot use it.)


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Grimbal
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Re: integer grid
« Reply #1 on: Nov 30^{th}, 2013, 3:00am » 
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Looks like an IBM Ponder This problem


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rmsgrey
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Re: integer grid
« Reply #2 on: Nov 30^{th}, 2013, 7:09am » 
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Immediate observations: The average value in a cell must be a little over 2.5. The largest integer you can use is 5, and it looks like you need to. You can replace the problem with the equivalent one with nonnegative integers (so you must have a 0 next to each larger number) and a target total of 57. It may or may not be easier to work with that version.


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antkor
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Posts: 30


Re: integer grid
« Reply #3 on: Dec 1^{st}, 2013, 6:53am » 
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rmsgrey is correct about what he says. Although, i am not aware of the variation he suggests. The challenge is of course to create the grid. I have managed to do it, but up to now i am breaking the rule once. I haven't managed to solve it perfectly, even though I am pretty sure it can be done. I am not aware of any logical way that gives the answer, so I suspect the only way of solving it is to brute force it.


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