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(035) O4

Part of 1983 Tournament Of Towns

Problems(1)

TOT 035 1983 Spring J-O4 different permutations of same digits, sum of digits

Source:

8/18/2019
The natural numbers MM and KK are represented by different permutations of the same digits. Prove that
(a) The sum of the digits of 2M2M equals the sum of the digits of 2K2K. (b) The sum of the digits of M/2M/2 equals the sum of the digits of K/2K/2 (M,KM, K both even). (c) The sum of the digits of 5M5M equals the sum of the digits of 5K5 K.
(AD Lisitskiy)
number theorypermutationsDigitssum of digitscombinatorics