Combinations

problem
Hamilton's puzzle

Age

7 to 11

Challenge level

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?
problem
More and more buckets

Age

7 to 11

Challenge level

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
problem
Those tea cups

Age

7 to 11

Challenge level

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.
problem
Human food

Age

7 to 14

Challenge level

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?
problem
Sealed solution

Age

7 to 14

Challenge level

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?
problem
Tea cups

Age

7 to 14

Challenge level

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.
problem
More children and plants

Age

7 to 14

Challenge level

This challenge extends the Plants investigation so now four or more children are involved.
problem
More plant spaces

Age

7 to 14

Challenge level

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.
problem
Dicing with numbers

Age

11 to 14

Challenge level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?
problem
Colour building

Age

11 to 14

Challenge level

Using only the red and white rods, how many different ways are there to make up the other rods?