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Product Of Ones

Problem

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

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