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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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What is the units digit for the number 123^(456) ?

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N000ughty Thoughts

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the number of noughts in 10 000! and 100 000! or even 1 000 000!

Weekly Problem 50 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1
Al and Bertie have £55 between then, so Chris and Di have £150-£55=£95 between then. As Al and Chris have £65 between them, the difference between the amounts Al and Di have is £95-£65, so £30.

This problem is taken from the UKMT Mathematical Challenges.

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