Sunday Times Brainteaser 1318
by Victor Bryant
Published 6th December 1987 (link)
In this letters-for-digits puzzle, as usual, different letters consistently replace different digits. I have thought of a two-digit number and worked out a fraction (in its lowest form) involving my number. The recurring decimal which I get consists of infinite repeats, i.e.:
? / MY = 0. REPEAT REPEAT …
Find the value of PART?
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BRG permalink1234567891011from itertools import permutations# ? * 999999 == MY * REPEATfor A, E, P, R, T in permutations(range(10), 5):repeat = 10 * (10 * (10 * (10 * (10 * R + E) + P) + E) + A) + Tfor M, Y in permutations(set(range(10)) - {A, E, P, R, T}, 2):if not (que := divmod((my := 10 * M + Y) * repeat, 999999))[1]:PART = 10 * (10 * (10 * P + A) + R) + Tprint(f"{que[0]}/{my} = 0.({repeat}) ==> {PART = }")
