# Representation - October 2008, Stage 3&4

## Problems

### Crossed Ends

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

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

### Legs Eleven

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

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

### Domino Square

##### Age 7 to 16 Challenge Level:

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

### Differences

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

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

### Tet-trouble

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

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

### Hexy-metry

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

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

### Napoleon's Theorem

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

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?