Elysia Hole (a teacher in Brighton) recently sent me an arithmetic procedure that she thought had the potential to develop into an inquiry. I think an appropriate prompt from her explanation (below) would be something similar to: With this prompt students can re-trace the procedure for themselves and proceed to questions about other numerical cases and the algebraic representation. Elysia's explanation is as follows: Pick any
digit and write it down three times. You'll now be looking at something like
"333" or "888". Add those three digits together: 3 + 3 + 3
= 9 or 8 + 8 + 8 = 24. Then divide the three-digit number by the sum of its
digits... always gives 37 as the answer.
You can do the same trick with four digits and always get the less pleasant answer 1,111 ÷ 4 = 277.75. The next whole number answer is typing the same digit nine times and then dividing it by the sum of its digits. This has the rather pleasing answer of 111,111,111 ÷ 9 = 12,345,679. This answer is missing an “8” but that can be fixed by squaring 111,111,111 which will give you the answer 12,345,678,987,654,321. That’s probably a whole new pattern to investigate that I'm not sure yet how it works. |

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