Sunday Times Teaser 3209 – All in Order
by Victor Bryant
Published Friday March 22 2024 (link)
Audley’s age is a two-figure number. He has that number of cards and on them he has spelt out the consecutive numbers from one up to and including his age, (“one”, “two”, etc) with one number on each card. Then he has arranged the cards in a row in alphabetical order. It turns out that two of the numbers are in the “correct” place; ie in the same place as if he had arranged the cards in numerical order).
If he had done all this a year ago, or if he repeated this whole exercise in a year’s time, there would be no card in the correct place.
How old is he?
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BRG permalink1234567891011121314151617# convert an integer in the range 1..99 into wordsun = (f"z one two three four five six seven eight nine "f"ten eleven twelve thirteen fourteen").split()ut = 'twen thir for fif six seven eigh nine onehundred'.split()i2w = lambda n: (un[n] if 0 < n < 15 else (ut[n - 12] + 'teen' if n < 20else ut[n // 10 - 2] + 'ty' + (' ' + un[n % 10] if n % 10 else '')))# collect the number of correct positions for each age <n>vals = {n:sum(a == b for a, b in zip(range(1, n + 1),sorted(range(1, n + 1), key=i2w))) for n in range(9, 101)}# look for (0, 2, 0) age sequencesfor n, v in vals.items():if v == 2 and vals.get(n - 1, -1) == vals.get(n + 1, -1) == 0:print(f"Audley is {n}.")
