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MathNet 2003 — Part 01 Question 23

Math Olympiad Vault · MathNet 2003 — Part 01

Question 23

All new-digit natural numbers that use exclusively the digits $1$, $2$ and $3$ are considered (the smallest is $111111111$ and the largest is $333333333$). Each of these numbers is written on a card; If you have a pack of $19683$ cards.

David, Juan and Pablo divide the cards according to the following rules: if the cards are from the same chic, then at least one of the new positions has the same digit.

If David has $133221311$ and Juan has $133211311$, determine which of the three guys have $123123123$.