Representation - October 2008, Stage 2&3

Problems

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Biscuit Decorations

Stage: 1 and 2 Challenge Level: Challenge Level:1

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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Ladybird Box

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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Three Squares

Stage: 1 and 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the greatest number of squares you can make by overlapping three squares?

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Five Coins

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Ben has five coins in his pocket. How much money might he have?

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Quadrilaterals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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Crossed Ends

Stage: 3 Challenge Level: Challenge Level:1

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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Legs Eleven

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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Domino Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

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Differences

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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