Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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....?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
This challenge is about finding the difference between numbers which have the same tens digit.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you find the chosen number from the grid using the clues?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
This dice train has been made using specific rules. How many different trains can you make?
An activity making various patterns with 2 x 1 rectangular tiles.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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.
These practical challenges are all about making a 'tray' and covering it with paper.
How many triangles can you make on the 3 by 3 pegboard?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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!