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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 รท 360. How did this help?
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
What is the remainder when 2^{164}is divided by 7?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Here are many ideas for you to investigate - all linked with the number 2000.