Factors and multiples
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problemFavouriteFind the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n. -
problemFavouriteEm'power'ed
Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem? -
problemFavouriteFac-Finding
Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful. -
problemFavouriteBiscuit Decorations
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
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problemFavouriteShare Bears
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
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problemFavouriteSame Length Trains
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
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problemFavouriteClapping Times
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
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problemFavouriteI Like ...
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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problemFavouriteOur Numbers
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?