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Euromaths

11 to 14

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?

problem

Digit sum

14 to 16

What is the sum of all the digits in all the integers from one to one million?

problem

Table total

14 to 16

Can you find the sum of all of the numbers in the table?

problem

Euler's squares

14 to 16

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

problem

Sangaku

16 to 18

The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.

problem

Beads

7 to 11

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

problem

Cyclic triangles

16 to 18

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

problem

Number squares

5 to 11

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

problem

Von Koch curve

16 to 18

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

problem

Favourite

Elevenses

11 to 14

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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Euromaths

Digit sum

Table total

Euler's squares

Sangaku

Beads

Cyclic triangles

Number squares

Von Koch curve

Elevenses