Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three
square grid, so that there is only one of each colour in every row
and every column
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Can you fit the tangram pieces into the outline of Granma T?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Solve the system of equations
xy = 1
yz = 4
zx = 9
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
Gravity on the Moon is about 1/6th that on the Earth. A
pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth.
How high a pole could he clear on the Moon?
In turn 4 people throw away three nuts from a pile and hide a
quarter of the remainder finally leaving a multiple of 4 nuts. How
many nuts were at the start?
What is the value of the integers a and b where sqrt(8-4sqrt3) =
sqrt a - sqrt b?
Ten squares form regular rings either with adjacent or opposite
vertices touching. Calculate the inner and outer radii of the rings
that surround the squares.