There are 25 grouchy people who live in the squares of a five-by-five grid. We’re gonna number the squares, starting in the upper left-hand corner, 1 through 25. The first row starts with one, the second row starts with six, the third row starts with 11, and so forth. Remember, each person is crabby toward his adjacent neighbor. Not his diagonal neighbor, but the person up or down or left or right of him. Each aspires to move into the apartment of his adjacent neighbor.
The question is very simple: What is the fewest number of total moves that can accomplish this?
February 27th, 2013 | Category: 
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64
Honestly, the correct answer is eluding your faithful Riddle Dude. 64 may be correct, but you must show the math or explain your answer for me here.
It is not possible for everyone to move into an adjacent square. Numbered the way you suggest, all of the neighbours of the odd numbers are even numbers and visa-versa. Since there are 13 odd numbers but only 12 even numbers in the apartment setup, it is not possible for the 13 odd numbers to all end up in even numbered apartments.
Thank you Brent for figuring this one out. My fellow riddle dude Joey passed away this year and I don’t know all of the solutions. Certainly today’s winner!