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.
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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?
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.
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.
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.?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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
An activity making various patterns with 2 x 1 rectangular tiles.
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?
This activity investigates how you might make squares and pentominoes from Polydron.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
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?
In how many ways can you stack these rods, following the rules?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
In this matching game, you have to decide how long different events take.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
The pages of my calendar have got mixed up. Can you sort them out?
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.
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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....?
Find out what a "fault-free" rectangle is and try to make some of
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
This dice train has been made using specific rules. How many different trains can you make?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Use the differences to find the solution to this Sudoku.
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.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
A Sudoku with clues as ratios.