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Programming Enigma Puzzles
From New Scientist #1785, 7th September 1991 [link]
My niece (whose age is a two-figure number) is very good at arithmetic, and to keep her occupied on a recent train journey I asked her to find a number with all its digits different and with the sum of its digits a multiple (more than one times) of her age.
She wrote down a list of lots of number with both those properties. So I then asked her to add 1 to each of her numbers, and to pick out from the new list each number which still had all its digits different and with the sum of its digits equal to a multiple (again, more than one times) of her age next birthday.
There were still quite a few numbers in this new list which had these properties. So I asked her to find one of them which, when multiplied by her age, gave an answer which still had all its digits different — which she did!
How old is she?