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

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

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

Football Crazy Hockey Mad

Age

11 to 14

Challenge level

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.
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?
problem

Flight of the Flibbins

Age

11 to 14

Challenge level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?