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

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Found problems: 3

1986 Tournament Of Towns, (119) 1
We are given two two-digit numbers , $x$ and $y$. It is known that $x$ is twice as big as $y$. One of the digits of $y$ is the sum, while the other digit of $y$ is the difference, of the digits of $x$ . Find the values of $x$ and $y$, proving that there are no others.
digit 2-digit number theory sum difference digits

1956 Moscow Mathematical Olympiad, 321
Find all two-digit numbers $x$ the sum of whose digits is the same as that of $2x$, $3x$, ... , $9x$.
sum of digits 2-digit number theory digits

1945 Moscow Mathematical Olympiad, 093
Find all two-digit numbers $\overline {ab}$ such that $\overline {ab} + \overline {ba}$ is a perfect square.
2-digit number theory perfect square perfect squares