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January 1st, 2017, 08:24 AM   #1
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Math Problem Requiring Thinking

A k-city is a k by k grid of positive integers so that every integer greater than 1 is the sum of one integer from the same row and one integer from the same column. Below is an example of a 3-city:

1 1 2
2 3 1
6 4 1

Make a 5-city that has an integer that is greater than or equal to 150.
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January 1st, 2017, 10:20 AM   #2
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you've posted this 3 times now.

I looked at it for a bit, didn't make any progress.

I imagine others have done the same.

Sometimes we don't have the answers.
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January 1st, 2017, 06:07 PM   #3
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Sorry. I thought that the algorithm of the website might have pushed the thread to the bottom where many people wouldn't see it. Won't happen again.
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January 2nd, 2017, 09:55 AM   #4
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This is the way I would set it up (think about it):

Let $\displaystyle a_{ij}$ be a typical grid element.
Then $\displaystyle a_{ij}=a_{ik}+a_{mj}, \ k\neq i, m\neq j$
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