Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Can you use the information to find out which cards I have used?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
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.
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Can you substitute numbers for the letters in these sums?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Ben has five coins in his pocket. How much money might he have?
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 the statements, can you work out how many of each type of
rabbit there are in these pens?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a 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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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!
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight 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?
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.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This challenge is about finding the difference between numbers which have the same tens digit.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
This dice train has been made using specific rules. How many different trains can you make?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
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?
Number problems at primary level that require careful consideration.
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?