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.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge is about finding the difference between numbers which have the same tens digit.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Find all the numbers that can be made by adding the dots on two dice.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
This dice train has been made using specific rules. How many different trains can you make?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
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 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?
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?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Ben has five coins in his pocket. How much money might he have?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you substitute numbers for the letters in these sums?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?