I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?
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?
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
Find all the numbers that can be made by adding the dots on two dice.
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
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?
Try grouping the dominoes in the ways described. Are there any left
over each time? Can you explain why?
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?
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
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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
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?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Can you fill in the empty boxes in the grid with the right shape
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
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.
This challenge extends the Plants investigation so now four or more children are involved.
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