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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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Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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Card Trick 2

Can you explain how this card trick works?


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

Choose any 4 whole numbers, for example (100, 2, 37, 59). Now take the difference between consecutive numbers, always subtracting the smaller from the larger, and ending with the difference between the first and the last numbers. What happens when you repeat this process over and over again? For example, continue the sequence of 4-tuples:

(100, 2, 37, 59), (98, 35, 22, 41), (63, 13, 19, 57), (50, 6, 38, 6) , ...

Investigate starting with different sets of 4 numbers.

What happens when you use 3 numbers, or 5, or 6, or 7 or 8 numbers?