RU-ALLRUSSIAN 1967 Problem 2
(a) The digits of a natural number are rearranged and the resultant number is added to the original number. Prove that the answer cannot be 99 ... 9 (1999 nines).
(b) The digits of a natural number are rearranged and the resultant number is added to the original number to give . Prove that the original number was divisible by 10.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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