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Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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How many zeros are there at the end of the number which is the product of first hundred positive integers?

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Enriching Experience

Find the five distinct digits N, R, I, C and H in the following nomogram

Rachel's Problem

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it true that $ 99^n $ has $ 2n $ digits and $ 999^n $ has $ 3n $ digits? Investigate!

(This problem was inspired by Rachel Galley's work on the problem called Giants in the June 1999 Six.)