Simultaneous equations

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
Pair squares

Age

16 to 18

Challenge level

The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.
problem
Escriptions

Age

16 to 18

Challenge level

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
problem
Quadratic harmony

Age

16 to 18

Challenge level

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
problem
Nine, ten and one

Age

11 to 14

Challenge level

Can you find the value of t in these equations?
problem
Intersection Sudoku 2

Age

11 to 16

Challenge level

A Sudoku with a twist.
problem
Simultaneous equations Sudoku

Age

11 to 18

Challenge level

Solve the equations to identify the clue numbers in this Sudoku problem.
problem
All-variables Sudoku

Age

11 to 18

Challenge level

The challenge is to find the values of the variables if you are to solve this Sudoku.
problem
Quadruple clue Sudoku

Age

11 to 16

Challenge level

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
problem
Colour islands Sudoku

Age

11 to 14

Challenge level

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.