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. . . .
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.
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
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?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
Four jewellers share their stock. Can you work out the relative values of their gems?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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?
Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6
Can you find the values at the vertices when you know the values on
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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
A Sudoku with a twist.
Solve the equations to identify the clue numbers in this Sudoku problem.
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 ?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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. . . .
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.
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
Change one equation in this pair of simultaneous equations very
slightly and there is a big change in the solution. Why?
When I park my car in Mathstown, there are two car parks to choose
from. Which car park should I use?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
Add up all 5 equations given below. What do you notice?
Solve the system and find the values of a, b, c , d and e.
b + c + d + e = 4
a + c + d + e = 5
a + b + d + e = 1
a + b + c + e = 2
a + b. . . .
Can you make a tetrahedron whose faces all have the same perimeter?
Solve the system of equations
xy = 1
yz = 4
zx = 9
There are lots of different methods to find out what the shapes are worth - how many can you find?
Can you work out how many of each kind of pencil this student
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?
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
Which is bigger, n+10 or 2n+3? Can you find a good method of
answering similar questions?
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.