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Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

Out of Line

Stage: 3 Short Challenge Level: Challenge Level:1
The starred square contains a B.

The square marked in yellow in the diagram on the right must be a D, since it is in the same row as B and E, and the same column as A and C.

The square marked in yellow must contain a B, as it is in the same column as A, D and B, and is in the same diagonal as E.

Consider the top row. This must have one of each of the letters in it, so in particular it must contain a B. The right-hand-most square is in the same column as the green B. The square to the left of this is in the same diagonal as this green B. The left-hand-most square is in the same diagonal as the black B. This means only the yellow square can contain the B.

Alternatively, you could use similar logic looking at the second column.

This problem is taken from the UKMT Mathematical Challenges.
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