Combinations

problem
Sweets in a box

Age

7 to 11

Challenge level

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?
problem
Halloween investigation

Age

7 to 11

Challenge level

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 make?
problem
Buying a balloon

Age

7 to 11

Challenge level

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?
problem
Super value shapes

Age

7 to 11

Challenge level

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 given totals?
problem
Cat food

Age

7 to 11

Challenge level

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 triangular stacks?
problem
Penta post

Age

7 to 11

Challenge level

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?
problem
Chocs, mints, jellies

Age

7 to 11

Challenge level

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?
problem
Polo square

Age

7 to 11

Challenge level

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
problem
The money maze

Age

7 to 11

Challenge level

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
problem
Butterfly cards

Age

7 to 11

Challenge level

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 want?