Enigma 1308: Passing through
19 July 2014
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From New Scientist #2466, 25th September 2004
If you are told to draw a rectangle along the lines of a sheet of graph paper such that its area is 40 squares you could choose rectangles measuring 8×5, 10×4, 20×2 or 40×1. Whether you chose the 8×5 or the 10×4 you would find that a diagonal drawn across your rectangle would pass though 12 of the squares.
(1) What is the smallest number of squares of the graph paper that can be the area of THREE different rectangles whose diagonals each pass through the same number of squares?
(2) How many squares does each of those diagonals pass through?