Simultaneous equations

problem
Favourite

LCM Sudoku II

Age

14 to 16

Challenge level

3 out of 3

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
problem
Favourite

Intersections

Age

14 to 18

Challenge level

1 out of 3

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
problem
Favourite

Always Two

Age

14 to 18

Challenge level

2 out of 3

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
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Favourite

Leonardo's Problem

Age

14 to 18

Challenge level

3 out of 3

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
problem
Favourite

Quadratic Harmony

Age

16 to 18

Challenge level

1 out of 3

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

Rudolff's Problem

Age

14 to 16

Challenge level

1 out of 3

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?
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Escriptions

Age

16 to 18

Challenge level

1 out of 3

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
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Battery Modelling

Age

16 to 18

Challenge level

1 out of 3

Find out how to model a battery mathematically
problem

Coffee

Age

14 to 16

Challenge level

2 out of 3

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

All Square

Age

11 to 14

Challenge level

2 out of 3

Solve the system of equations xy = 1 yz = 4 zx = 9