MathDB

3

Part of 2021 German National Olympiad

Problems(1)

Sums of cubes of numbers with certain digits are equal

Source: Germany 2021, Problem 3

6/16/2021
For a fixed kk with 4≤k≤94 \le k \le 9 consider the set of all positive integers with kk decimal digits such that each of the digits from 11 to kk occurs exactly once.
Show that it is possible to partition this set into two disjoint subsets such that the sum of the cubes of the numbers in the first set is equal to the sum of the cubes in the second set.
algebrasum of cubesalgebra proposedcombinatorics proposedDigitsDigit