A friend spotted this and knew I would be interested.
Something very exciting happened last Friday when one of my pupils, Chika Ofili, popped into the classroom and asked if he could tell me something he had thought of over the summer holidays. I was intrigued. I had given him a book called First Steps for Problem Solvers (published by the UKMT) to look at over the holidays and inside the book was a list of the divisibility tests, which are used to quickly work out whether a number is exactly divisible by either 2, 3, 4, 5, 6, 7, 8 or 9 before you actually start dividing. Except that there was no test listed for checking divisibility by 7. The reason why it was missing is because there is no easy or memorable test for dividing by 7, or so I thought!
In a bored moment, Chika had turned his mind to the problem and this is what he came up with. He realised that if you take the last digit of any whole number, multiply it by 5 and then add this to the remaining part of the number, you will get a new number. And it turns out that if this new number is divisible by 7, then the original number is divisible by 7. What an easy test!
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