Friday, October 14, 2005

NPR Sunday Puzzle (Oct 16) - Multiplication Magic Square

NPR Sunday Puzzle (Oct 16) - Multiplication Magic Square
Q: In a standard 4 by 4 magic square you arrange the digits from one to sixteen so each row, column and corner diagonal totals 34. This is a multiplication magic square: Arrange sixteen numbers in a four by four square so that the product of each row, column and corner to corner diagonal is 5,040. You can use any numbers you want. But they have to be whole numbers and you can't repeat a number in the square. (And as a hint I'll tell you the number in the upper left corner is 42.)
Finally! A mathematical/number puzzle instead of a word puzzle! I do have an answer to the puzzle. In fact I have several since the answer is non-unique. In addition to solutions that have 42 in the upper left, and solutions that have 42 elsewhere in the puzzle, I found solutions that don't have 42 at all! As usual, I won't post any answers until after the deadline. My one hint: prime factorization.
Edit: Okay, after all that work and no one called me from NPR. Check the following PDF for the solution(s).
Magic Square Answer(s)
Edit: Since this posting, I've found 8 other arrangements that I previously missed (with 30 in them). That brings the total to 80, not 72.


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