Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
How many six digit numbers are there which DO NOT contain a 5?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?
Using only the red and white rods, how many different ways are
there to make up the other colours of rod?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
An environment which simulates working with Cuisenaire rods.
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?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
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?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Eight children enter the autumn cross-country race at school. How
many possible ways could they come in at first, second and third
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
A little mouse called Delia lives in a hole in the bottom of a
tree.....How many days will it be before Delia has to take the same
Here is a collection of puzzles about Sam's shop sent in by club
members. Perhaps you can make up more puzzles, find formulas or
find general methods.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
Sam displays cans in 3 triangular stacks. With the same number he
could make one large triangular stack or stack them all in a square
based pyramid. How many cans are there how were they arranged?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Semaphore is a way to signal the alphabet using two flags. You
might want to send a message that contains more than just letters.
How many other symbols could you send using this code?
Four children were sharing a set of twenty-four butterfly cards.
Are there any cards they all want? Are there any that none of them
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?