Combinations

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
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
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
Button-up some more

Age

7 to 11

Challenge level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
problem
The Olympic torch tour

Age

14 to 16

Challenge level

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?
problem
Button-up

Age

5 to 7

Challenge level

My coat has three buttons. How many ways can you find to do up all the buttons?
problem
Colourful tiles

Age

11 to 14

Challenge level

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?
problem
Almost constant digits

Age

11 to 14

Challenge level

How many 10-digit numbers containing only 1s, 2s and 3s can you write?
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
Island hopping

Age

11 to 14

Challenge level

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?