Counting

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Binomial coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
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EYFS thinking about: Sunflower numbers

Here are some examples of children's thinking prompted by drawings of numbered sunflowers on an outside wall.
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Doodles

Age

14 to 16

Challenge level

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
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Euler's officers

Age

14 to 16

Challenge level

How many different ways can you arrange the officers in a square?
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How many dice?

Age

11 to 14

Challenge level

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
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Euromaths

Age

11 to 14

Challenge level

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?
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Ruler

Age

16 to 18

Challenge level

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?
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1 to 8

Age

7 to 11

Challenge level

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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Diagonal sums Sudoku

Age

7 to 16

Challenge level

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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Loose change

Age

11 to 14

Challenge level

In how many ways can you give change for a ten pence piece?