10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Can you use this information to work out Charlie's house number?
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.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Six friends sat around a circular table. Can you work out from the
information who sat where and what their profession were?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
An activity making various patterns with 2 x 1 rectangular tiles.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
How many trapeziums, of various sizes, are hidden in this picture?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?