Sunday Times Teaser 2586 – Powerful Dice
by Danny Roth
Published: 15 April 2012 (link)
George and Martha threw a dice, noted the number of spots on the uppermost face, and entered that number in one of the boxes of a 3-by-3 grid of nine squares. They repeated the exercise eight more times resulting in a number in each box.
Then George looked at the three 3-figure numbers read across the rows and commented that each was a square or a cube. Martha looked at the three 3-figure numbers read down the columns and said the same was true for her numbers. Furthermore, their two sets of three numbers had only one in common.
What (in increasing order) were the five different 3-figure numbers?
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Brian Gladman permalink12345678910111213141516171819202122from itertools import permutations# three digit squares with digits 1 to 6 onlysq = tuple(x ** 2 for x in range(10, 32)if all('0' < v < '7' for v in str(x ** 2)))# three digit cubes with digits 1 to 6 onlycu = tuple(x ** 3 for x in range(5, 10)if all('0' < v < '7' for v in str(x ** 2)))nb = sq + cufor rows in permutations(nb, 3):# convert row values to column valuescols = tuple(map(int, (''.join(x) for x in zip(*map(str, rows)))))# use symmetry to avoid duplicate solutionsif rows < cols:# form the set of all the numbersnbrs = tuple(sorted(set(rows) | set(cols)))if all(x in nb for x in cols) and len(nbrs) == 5:print('The numbers are:', nbrs)
