During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different symmetrical shapes can you make by shading triangles or squares?
A challenging activity focusing on finding all possible ways of stacking rods.
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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.?
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.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
This activity investigates how you might make squares and pentominoes from Polydron.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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
In how many ways can you stack these rods, following the rules?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
The pages of my calendar have got mixed up. Can you sort them out?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
In this matching game, you have to decide how long different events take.
Find out about Magic Squares in this article written for students. Why are they magic?!
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Use the differences to find the solution to this Sudoku.
This dice train has been made using specific rules. How many different trains can you make?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Four small numbers give the clue to the contents of the four
A Sudoku with a twist.
A Sudoku with clues as ratios.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?