Competition problem — Number theory

Library / /627 of 1394

Number theory Difficulty 5.2 AIME, harder Prove it United States

Problem:

Call a 9-digit number a cassowary if it uses each of the digits $1$ through $9$ exactly once. Compute the number of cassowaries that are prime.

Solution

Solution:

Every cassowary is divisible by $3$ , as the sum of its digits is $1 + 2 + \dots + 9 = 45$ . Since all such numbers are divisible by $3$ and greater than $3$ , none of them are prime. So, there are $0$ prime cassowaries.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.