Combinations

problem
Break it up!

Age

5 to 11

Challenge level

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
problem
Brailler

Age

11 to 14

Challenge level

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?
problem
Semaphore signals

Age

7 to 11

Challenge level

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?
problem
What shape and colour?

Age

5 to 7

Challenge level

Can you fill in the empty boxes in the grid with the right shape and colour?
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
Rod measures

Age

7 to 11

Challenge level

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?
problem
Clocked

Age

11 to 14

Challenge level

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?
problem
Beads

Age

7 to 11

Challenge level

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
problem
Two on five

Age

5 to 11

Challenge level

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
problem
Elf suits

Age

7 to 11

Challenge level

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?