Interactives

Four cards, a few cuts and turns, and the card you noted ends up facing the other way from the rest. Try it, then see why parity makes it unavoidable.

Ten cards, cut anywhere, turn the top two over, repeat. Watch an invariant hold, then fold the packet and find exactly five face up every time.

Reach a target arrangement of face-up and face-down cards using only cuts and turn-over-two moves. Some targets are impossible: can you tell which?

Ten high cards, paired and folded by a volunteer, and only the royal flush ends face up. See the odd/even bookkeeping that makes it work.

Slide a 2×2 window around a 4×4 grid of bits that wraps at the edges. Every position shows a different pattern: the idea behind position-coding in robotics.

Can a 4×4 grid give every cell a unique cross-shaped neighbourhood? Hunt for two matching crosses, or colour your own grid and watch the collision appear.