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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...


Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Where Can We Visit?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Two Much

Age 11 to 14
Challenge Level

Explain why the arithmetic sequence

1, 14, 27, 40, ...

contains many terms of the form 222...2 where only the digit 2 appears. How many twos appear in these terms?