## Product Of Zero

#### Problem

Take any 2-digit number and multiply the digits together. If this process is continued, all 2-digit numbers will become a single digit number.

For example, | 75: | 7 5 = 35, 3 5 = 15, 1 5 = 5 |

68: | 6 8 = 48, 4 8 = 32, 3 2 = 6 | |

45: | 4 5 = 20, 2 0 = 0 |

How many 2-digit numbers will finish on zero?

Problem ID: 37 (Mar 2001) Difficulty: 1 Star