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## Prime Nine

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #40004 Fun: (2.56) Difficulty: (1.97) Category: Probability Submitted By: RampaginRobo

There are 9! ways to arrange the digits 1-9 to form a 9-digit number.

E.g. 345, 987, 126

If you know this, then if I wrote all 9! possibilities on cards (1 way per card), and I asked you to select one at random; what is the probability that the number you selected is prime?

Zero.

A well known divisibility rule is that if a number's digits add to 9, the number itself is a multiple of 9.

(E.g. 18, 1+8=9, 18 is a multiple of 9
24786, 2+4+7+8+6=27, 2+7=9, 24786 is a multiple of 9)

Given the fact that 1+2+...+8+9=45, which is a multiple of 9; this means that all 9! numbers are multiples of 9.

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