An Example

Suppose we have many different "fruits" - apples, oranges, bananas etc. And we also have many different "baskets". Each basket has a label indicating what kinds of fruits that it can hold. E.g. If the label is "apples, oranges and pears", then the basket can hold these three kinds of fruits. The following are the three rules about labelling baskets: Rule 1 - For any two different fruits, there is exactly one basket that can hold them. Rule 2 - Any basket can hold at least two different fruits. Rule 3 - We can find three different fruits such that no basket can hold them together.

Warmup question 1

Suppose there are only three fruits: apples, oranges and pears. How many baskets should we need such that the three rules can be satisfied?

Warmup question 2

Now we have four fruits: apples, oranges, pears and bananas. Also we have 6 baskets. How can we label them such that the three rules can be satisfied?

A Quiz

After finishing the warmup questions, we will do a quiz. Go to this website