Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability intermediate

Problem

Dr. Math's four-digit house number contains no zeroes and can be split into two different two-digit primes ``'' and ``'' where the digits , , and are not necessarily distinct. If each of the two-digit primes is less than 40, how many such house numbers are possible?
Solution
The two-digit primes less than 40 are 11, 13, 17, 19, 23, 29, 31, and 37. Thus there are choices for the two-digit prime . Since and must be distinct, there are remaining choices for . Altogether, there are choices for and .
Final answer
56