The CountCraft cast
Each friend shows you one idea by how they act. Meet them all and see how the ideas fit together.
-
Tallis The Two-Ways Counter — counts the same collection along rows, then along columns, and insists the two totals be equal (double counting) -
Bijou The Pair-Matcher — draws a one-to-one pairing between two sets to prove they are exactly the same size (bijection) -
Stacia The Staircase-Mirror — mirrors a one-two-three staircase against itself to make a rectangle (triangular numbers) -
Nona The Gnomon-Grower — adds the next odd L-shaped layer to grow a square one ring at a time (perfect squares) -
Arel The Square-Cutter — cuts a square into four rectangles to read off a-squared plus two-a-b plus b-squared (area model) -
Domina The Domino-Tiler — tiles a strip with squares and dominoes and counts the number of ways (Fibonacci tilings) -
Chessa The Handshake-Counter — pairs everyone with everyone exactly once to count the handshakes (choose two) -
Cammy The Committee-Splitter — sorts every committee by whether the last person is in or out (Pascal's rule) -
Sett The Subset-Flipper — flips an in-or-out coin for each item to list every subset exactly once (two-to-the-n) -
Parry The Parity-Prover — two-colours a board to show when a tiling simply cannot exist (parity and impossibility) -
Quill The Proof Director — a warm, attentive adult who coaches build-the-two-counts-then-read-the-identity, and never proves for the kid