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 January 1st, 2017, 07:24 AM #1 Newbie   Joined: Dec 2016 From: New Jersey Posts: 7 Thanks: 1 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.
 January 1st, 2017, 09:20 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,931 Thanks: 999 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. Thanks from Joppy
 January 1st, 2017, 05:07 PM #3 Newbie   Joined: Dec 2016 From: New Jersey Posts: 7 Thanks: 1 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. Thanks from Joppy
 January 2nd, 2017, 08:55 AM #4 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,363 Thanks: 100 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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