## Product Of Ones

#### Problem

Thirty-seven is the smallest number we can multiply three by to produce a product consisting entirely of ones, 37 3 = 111.

What is the smallest number you can multiply seven by to produce a product consisting entirely of ones?

#### Solution

One method is to divide numbers in the sequence 111, 1111, 11111, ... , searching for an integral quotient.

Leading to | 111111 7 | = 15873 | being the first such value. |

Thirty-seven was the smallest number to multiply three to produce a product consisting of ones. What is the next such number?

Can you generalise?

What about for seven?

Problem ID: 23 (Nov 2000) Difficulty: 1 Star