Can you arrange a set of numbers in pairs, so that the sum of each pair is a perfect square? What if the sums must be primes? What if the sums must all be distinct? Discover the surprising variations in this simple challenge.

How many sheep can you place on a field, so that none can be attacked by the simple-minded wolf? What if there's more than one wolf?

Every journey has its costs and its rewards. Can you complete this one without any debt?

In how many ways can you draw a star using all the vertices of a polygon, without lifting your pencil from the paper? Are there some polygons for which it's not possible?

Explore the surprising variations in conceptually simple sequences of numbers, constructed by applying one of two operations to generate each successive term. Can you make the sequence return to its starting value?

What happens when generous people sit in a circle, and share candy – under some conditions – with each other?

Fold a long strip of paper in half several times. Can you see a pattern in the creases formed along the length of the paper? What sorts of route do we trace if we use the creases to direct our turns along a path?