[ Number Systems ]

Kaschei the Immortal guesses three two-digit numbers: $a, b$ and $с$. Ivan Tsarevich must name him three numbers: $X$, $Y, Z$, after which Kaschei will tell him the sum $a X+b Y+c Z$. Tsarevich must guess the guessed numbers, otherwise his head will be cut off. How can he save himself

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The Tsarevich must name the numbers $1, 100, 100^2 = 10000$. The numbers $a, b, c$ are the "digits" of Koshchei's answer in base 100. Send a comment

## Problem