Your Solutions - Stage 4 & 5

Take Three from Five

Age 11 to 16
Challenge Level

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Number Rules - OK

Age 14 to 16
Challenge Level

Can you produce convincing arguments that a selection of statements about numbers are true?

Always Perfect

Age 14 to 18
Challenge Level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Common Divisor

Age 16 to 18
Challenge Level

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?

Polite Numbers

Age 16 to 18
Challenge Level

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

Digital Equation

Age 16 to 18
Challenge Level

Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?

The Better Choice

Age 14 to 16
Challenge Level

Here are two games you can play. Which offers the better chance of winning?

Quadratic Matching

Age 14 to 16
Challenge Level

Can you match each graph to one of the statements?

Curve Hunter

Age 14 to 18
Challenge Level

This problem challenges you to sketch curves with different properties.

Curve Fitter

Age 14 to 18
Challenge Level

This problem challenges you to find cubic equations which satisfy different conditions.

Exploring Cubic Functions

Age 14 to 18
Challenge Level

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Curvy Equation

Age 16 to 18
Challenge Level

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.