# Calendar 2024

# 1.1 Tetrahedra

There are 2024 balls in a triangular pyramid 22 balls to a side.

20 balls in a pyramid 4 balls to a side depicted.

# 2.1 Dice

There are 2024 ways to roll 4 22-sided dice summing to 25.

56 ways to roll 4 6-sided dice summing to 9 depicted.

# 2.2 n-Dimensional Partitions

There are 2024 7-dimensional partitions of 6.

71 5-dimensional partitions of 4 depicted.

# 2.3 Toads And Frogs

It takes 2024 moves (of a slide or jump) to swap 44 toads with 44 frogs on a strip of 89 lily pads.

24 moves to swap 4 toads and 4 frogs on 9 lily pads depicted.

# 2.4 Tree Polyominoes

There are 2024 tree polyominoes with width 4 and height 4.

55 tree polyominoes with width 3 and height 3 depicted.

# 2.5 Triangles

There are 2024 triangles with integer sides with circumcircle radius 15 or less.

47 triangles with circumcircle radius 4 or less depicted.

# 2.6 Grid Links

There are 2024 ways to link elements of a 4x4 grid together, with anti-diagonals, with 0 or 2 neighbours each, without consecutive collinear links.

43 ways to link elements of a 3x3 grid depicted.

# 2.7 Chiral Bracelets

There are 2024 chiral bracelets with 4 red beads and 44 white beads.

35 chiral bracelets with 4 red beads and 11 white beads depicted.

# 2.8 Motifs

There are 2024 patterns of 5-motifs in \(\left(\mathbb{Z}_{12}\right)^2\).

26 patterns of 3-motifs depicted.

# 2.9 Walks

There are 2024 3-step self-avoiding walks on a 14x14 square.

44 walks on a 3x3 square depicted.

# 2.10 Quadrilaterals

There are 2024 quadrilaterals with integer sides with perimeter 47, modulo rotations.

35 quadrilaterals with perimeter 13 depicted.

# 2.11 Coloured Partitions

There are 2024 partitions of a 6-set into coloured blocks with exactly 2 colours used.

64 partitions of a 4-set with 2 colours depicted.

# 2.12 Bishop Moves

There are 2024 possible bishop moves on a 12x12 chessboard (depicted)