## Problems

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

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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

Can you cut up a square in the way shown and make the pieces into a
triangle?

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

Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?

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

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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

Can you fit the tangram pieces into the outline of this plaque design?

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

A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?

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

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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

Replace the letters with numbers to make the addition work out
correctly. R E A D + T H I S = P A G E

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

A job needs three men but in fact six people do it. When it is
finished they are all paid the same. How much was paid in total,
and much does each man get if the money is shared as Fred suggests?

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

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

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

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

##### Age 11 to 18 Challenge Level:

Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?

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

Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
PQR?

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

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0
what can you say about the triangle?

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

Do you have enough information to work out the area of the shaded quadrilateral?

## Featured Solutions

## Articles & Games

Basic strategy games are particularly suitable as starting points
for investigations. Players instinctively try to discover a winning
strategy, and usually the best way to do this is to analyse the
outcomes of series of 'moves'. With a little encouragement from the
teacher, a mathematical investigation is born.