## Problems

##### Age 5 to 7 Challenge Level:

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of 3 dominoes?

##### Age 7 to 11 Challenge Level:

Use the information about the ducks on a particular farm to find
out which of the statements about them must be true.

##### Age 11 to 14 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

##### Age 11 to 14 Challenge Level:

If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?

##### Age 14 to 16 Challenge Level:

Explore the geometry of these dart and kite shapes!

##### Age 14 to 16 Challenge Level:

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

##### Age 14 to 16 Challenge Level:

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .

##### Age 16 to 18 Challenge Level:

Four circles all touch each other and a circumscribing circle. Find
the ratios of the radii and prove that joining 3 centres gives a
3-4-5 triangle.

##### Age 16 to 18 Challenge Level:

The sum of any two of the numbers 2, 34 and 47 is a perfect square.
Choose three square numbers and find sets of three integers with
this property. Generalise to four integers.

##### Age 16 to 18 Challenge Level:

Investigate the number of points with integer coordinates on
circles with centres at the origin for which the square of the
radius is a power of 5.

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