Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6
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 ?
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?
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.
Four jewellers possessing respectively eight rubies, ten saphires,
a hundred pearls and five diamonds, presented, each from his own
stock, one apiece to the rest in token of regard; and they. . . .
The challenge is to find the values of the variables if you are to
solve this Sudoku.
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.
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
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. . . .
Can you find the values at the vertices when you know the values on
When I park my car in Mathstown, there are two car parks to choose
from. Which car park should I use?
Which is bigger, n+10 or 2n+3? Can you find a good method of
answering similar questions?
Change one equation in this pair of simultaneous equations very
slightly and there is a big change in the solution. Why?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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. . . .
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?
Find the vertices of a pentagon given the midpoints of its sides.
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
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. . . .
Solve the equations to identify the clue numbers in this Sudoku problem.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
You need to find the values of the stars before you can apply normal Sudoku rules.
If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
A Sudoku with a twist.
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.
Solve the system of equations
xy = 1
yz = 4
zx = 9
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
There are lots of different methods to find out what the shapes are worth - how many can you find?
How many intersections do you expect from four straight lines ?
Which three lines enclose a triangle with negative co-ordinates for
every point ?
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
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.
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?
Can you work out how many of each kind of pencil this student
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?
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of