this month, Stage 3 & 4

October 2008

 

Problems

Why not send us your solutions?

problem Icon

Crossed Ends

Stage:3 Challenge Level:Challenge Level:1

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

problem Icon

Legs Eleven

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

problem Icon

Dozens

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Use the digits 1, 3, 4, 5 and one more digit and, with these digits, make the largest possible 5-digit number which is divisible by 12.

problem Icon

Tet-trouble

Stage:4 Challenge Level:Challenge Level:1

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

problem Icon

Differences

Stage:4 Challenge Level:Challenge Level:2Challenge Level:2

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

problem Icon

Hexy-metry

Stage:4 and 5 Challenge Level:Challenge Level:2Challenge Level:2

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

problem Icon

Napoleon's Theorem

Stage:4 and 5 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

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?