Five equations... five unknowns... can you solve the system?
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.
For any right-angled triangle find the radii of the three escribed
circles touching the sides of the triangle externally.
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
The challenge is to find the values of the variables if you are to
solve this Sudoku.
A Sudoku with a twist.
Solve the equations to identify the clue numbers in this Sudoku problem.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
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.
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.
Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter of rectangles to gain insight into the graphs.
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Can you find the values at the vertices when you know the values on the edges?
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
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?
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. . . .
There are lots of different methods to find out what the shapes are worth - how many can you find?
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz
+ zx = 3. What is the largest value that any of the numbers can
Find the exact values of x, y and a satisfying the following system
of equations: 1/(a+1) = a - 1 x + y = 2a x = ay
Four jewellers share their stock. Can you work out the relative values of their gems?
Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
Can you make a tetrahedron whose faces all have the same perimeter?
Change one equation in this pair of simultaneous equations very
slightly and there is a big change in the solution. Why?
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
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?
Crack this code which depends on taking pairs of letters and using
two simultaneous relations and modulus arithmetic to encode the
Find a quadratic formula which generalises Pick's Theorem.
Which is bigger, n+10 or 2n+3? Can you find a good method of
answering similar questions?
Plane 1 contains points A, B and C and plane 2 contains points A
and B. Find all the points on plane 2 such that the two planes are
If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of
these numbers must be 1. Now for the complexity! When are the other
numbers real and when are they complex?
When I park my car in Mathstown, there are two car parks to choose
from. Which car park should I use?
A bag contains red and blue balls. You are told the probabilities
of drawing certain combinations of balls. Find how many red and how
many blue balls there are in the bag.
Investigate the effects of the half-lifes of the isotopes of cobalt
on the mass of a mystery lump of the element.
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
Find out how to model a battery mathematically