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Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Statement Snap

Age 7 to 14 Challenge Level:

You might like to take a look at the problem Satisfying Statements together with the accompanying Teachers' Resources, as the game and the problem have been designed to complement one another.

You may wish to start your students off with the simplest scoring system, so that they can get used to the game, and then move on to the more challenging versions which might pique students' curiosity and generate interesting insights and discussions:

"If I know that 49 is a square number and a multiple of 7, then I know that 4900 is as well. Or 490000. Or 49000000..."

"If I know that 18, 38, 58, 78 and 98 are even but not multiples of 4, and 2 less than a multiple of 10, then so are 118, 138, 158, 178 and 198. Or 218, 238, 258, 278 and 298, or ..."