Diophantine equations

article
Why Stop at Three by One

Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.
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
problem

Coffee

Age

14 to 16

Challenge level

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?
problem

In Particular

Age

14 to 16

Challenge level

Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers?