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December 31st, 2016, 01:21 PM   #1
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From: New Jersey

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Really stuck on this. Please help.

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

Part 1: Make a 5-city that has an integer that is greater than or equal to 150.

Part 2: Show that for all k ≥ 1, the largest entry in a k-city is, at most, 3^ (k choose 2)
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