Enigma 1240: Stack ’em high
17 April 2015
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From New Scientist #2396, 24th May 2003 [link]
Joe’s daughter likes puzzles just as much as her father and spends quite some time designing her own.
Last weekend, while just fiddling with some standard dice, she worked out that she could stack them, one on one, so that the total obtained from the numbers on one face of the stack was the same for all four faces when she used the following rule:
Take the number on one face of the first dice, add to it twice the number on the corresponding face on the second dice, three times the number on the third dice, and so on.
She made a stack and showed it to her father. After some thought and a few calculations, Joe told her that by adding a few more dice his total would be six times hers.
How many extra dice did Joe have in mind?