Diophantine equations

problem
Favourite

Letter Land

Age

11 to 14

Challenge level

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
problem
Favourite

Fibs

Age

11 to 14

Challenge level

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
problem
Favourite

CD Heaven

Age

14 to 16

Challenge level

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?
problem

Rudolff's Problem

Age

14 to 16

Challenge level

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
problem

Some Cubes

Age

16 to 18

Challenge level

The sum of the cubes of two numbers is 7163. What are these numbers?
problem

Code to Zero

Age

16 to 18

Challenge level

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.
problem

Our Ages

Age

14 to 16

Challenge level

I am exactly n times my daughter's age. In m years I shall be ... How old am I?
problem

Double Angle Triples

Age

16 to 18

Challenge level

Try out this geometry problem involving trigonometry and number theory
problem

Lattice Points

Age

16 to 18

Challenge level

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?
problem

Exhaustion

Age

16 to 18

Challenge level

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2