## Problems

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

Can you go from A to Z right through the alphabet in the hexagonal
maze?

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

Follow the journey taken by this bird and let us know for how long
and in what direction it must fly to return to its starting point.

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

Without taking your pencil off the paper or going over a line or
passing through one of the points twice, can you follow each of the
networks?

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

July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When
did July 1st fall on a Monday again?

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

A little mouse called Delia lives in a hole in the bottom of a
tree.....How many days will it be before Delia has to take the same
route again?

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

Can you go through this maze so that the numbers you pass add to exactly 100?

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?

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

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

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

Given a square ABCD of sides 10 cm, and using the corners as
centres, construct four quadrants with radius 10 cm each inside the
square. The four arcs intersect at P, Q, R and S. Find the. . . .

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

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

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

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

##### Age 14 to 18 Challenge Level:

Here is a pattern composed of the graphs of 14 parabolas. Can you
find their equations?

##### Age 14 to 18 Challenge Level:

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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