Prime Order
Weekly Problem 24 - 2006
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
Age
11 to 14
Challenge level
Problem
How many of the three-digit numbers that can be made from all of the digits 1, 3 and 5 (used only once each) are prime?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: None of them are prime
Numbers whose digits add up to a multiple of 3 are multiples of 3 (and numbers whose digits add up to a multiple of 9 are multiples of 9).
1 + 3 + 5 = 9, so any combination of the digits 1, 3, 5 will be a multiple of 3 (and 9).