This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 2

1989 All Soviet Union Mathematical Olympiad, 494
Tags: sum of squares , 5-digit , subset , algebra , number theory
Show that the $120$ five digit numbers which are permutations of $12345$ can be divided into two sets with each set having the same sum of squares.

1970 All Soviet Union Mathematical Olympiad, 141
Tags: number theory , digit , 5-digit
All the $5$-digit numbers from $11111$ to $99999$ are written on the cards. Those cards lies in a line in an arbitrary order. Prove that the resulting $444445$-digit number is not a power of two.