Enigma 1625: Diagonal diversion
14 December 2011
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From New Scientist #2790, 11th December 2010 [link]
A niece, Amy, asks me to help her revise some arithmetic, her favourite subject, so we make 25 cards numbered consecutively from 1 to 25, which we shuffle and deal out in a 5-by-5 grid. She then multiplies together the numbers in each row and writes the product at the end of the row; we call these products A to E, top to bottom. Amy then repeats the process for the columns, and these are the products F to J, left to right. Having got all these correct, she decides to find the product for the leading diagonal (top left to bottom right), and she calls this K.
Given that A = 483840, B = 604032, C = 90440, D = 57960, F = 193375, G = 1530144, H = 288000, I = 258552, what value should Amy obtain for K?