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.?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
What could the half time scores have been in these Olympic hockey
Can you find the chosen number from the grid using the clues?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
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
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 the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
How many trapeziums, of various sizes, are hidden in this picture?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
My coat has three buttons. How many ways can you find to do up all
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
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.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?