MathDB

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

Source:

August 18, 2019

number theorypermutationsDigitssum of digitscombinatorics

Problem Statement

The natural numbers

M

and

K

are represented by different permutations of the same digits. Prove that
(a) The sum of the digits of

2M

equals the sum of the digits of

2K

. (b) The sum of the digits of

M/2

equals the sum of the digits of

K/2

(

M, K

both even). (c) The sum of the digits of

5M

equals the sum of the digits of

5 K

.
(AD Lisitskiy)