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Choose any three by three square of dates on a calendar page...

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Card Trick 2

Can you explain how this card trick works?

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Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Latin Numbers

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

If you haven't already done so, take a look at the shaded image at the bottom of the problem.

If the bottom row is 6N, what can you deduce about the first digit of N?

If the fifth row is 5N, what can you deduce about the last digit in that row?

What can you say about the last digit of 2N, 4N and 6N?