Cards and Math
Discover mathematical principles and probability theory through card games and interactive demonstrations.
Baby Hummer
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.
Cut and Turn Over
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.
CATO Target Puzzle
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?
Royal Flush Hummer
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.
de Bruijn Torus
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.
Cross Window Puzzle
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.
de Bruijn Comb
A comb exposes four of eight positions as it slides along a 16-bit cycle. Watch all sixteen four-bit reads come out distinct.
DNA and the de Bruijn Graph
Type a DNA string, see which triplets light up on the sequencing array, and watch an Euler path through the de Bruijn graph read the sequence back.
Middle Layer Graph
Explore the graph of r-sets and (r+1)-sets of a (2r+1)-element set, joined by containment: the setting of the middle levels conjecture.
Order Matters
Cut a 48-card stack as often as you like, deal three, and once the spectators line up low to high the performer names all three cards. A de Bruijn cycle of colours and orders.
Partitioning People
Five spectators take five cards and group themselves by suit. Every possible grouping appears exactly once in the cycle, so the performer knows where the deck was cut.
Lie Detector
Riffle-shuffle a red-black deck and a performer still knows which colour you are lying about. The Gilbreath principle, played out card by card.
A Mind-Reading Effect
Twenty-five cards, one riffle shuffle and two deals into five piles, and the arrangement survives. A Gilbreath effect you can step through.
The Gilbreath Principle
Deal off some cards, riffle them back into the rest, and see which properties of the original order survive the shuffle: all four parts of the theorem, live.
The Packet as a Computer
Deal a twelve-card packet into any number of piles, shuffle in a few fixed ways, cut anywhere: the packet still computes your card.
Perfect Shuffles
In-shuffles and out-shuffles on twenty cards, one at a time. Follow a card, count the cycle, and see why eight out-shuffles restore a full deck.
Monge and Milk Shuffles
Over-and-under versus top-and-bottom: two classic shuffles that undo each other, animated card by card on a twenty-card deck.