Combinatorics
Counting principles180 problems · 14 skills
Bits and binary trees 4Counting in lists and arrays 4🔒Counting principle 17🔒Handshakes 18🔒Integer pairs with bounded product 5🔒Licence plates 6🔒Numbers and codes with digit rules 17🔒Numbers containing a digit 17🔒Numbers from digit cards 18🔒Outfits and selections 15🔒Parity and odd sums 17🔒Stacking blocks 13🔒Vowels and consonants 12🔒Words and strings with restrictions 17🔒
Permutations and arrangements113 problems · 7 skills
Arrangements of letters 17Choosing officers 14🔒Circular arrangements of colours 11🔒Derangements and fixed points 18🔒Lines with restrictions 18🔒Ordering items 18🔒Seating arrangements 17🔒
Combinations and selections115 problems · 7 skills
Choosing with gaps 17Committees 17🔒Pairs and matchings 14🔒Pascal's triangle 18🔒Splitting into groups 18🔒Teams and lineups 13🔒nCr and nPr formulas 18🔒
Distributing objects59 problems · 4 skills
Distributing objects into boxes 17Integer solutions with conditions 18🔒Monotone lists and functions 6🔒Sequences and compositions 18🔒
Sets and Venn diagrams111 problems · 7 skills
Counting relations and functions 18Counting subsets 15🔒Minimum overlap of percentages 12🔒Parameters from set conditions 18🔒Three sets 13🔒Two sets 17🔒Unions and intersections 18🔒
Pigeonhole and extremal problems177 problems · 13 skills
Coloured beads and balloons 18Coprime subsets 12🔒Divisibility chains 18🔒Extremal counting 17🔒Families of sets 12🔒Forcing a sum condition 14🔒Guaranteed minimum 18🔒Maximum sums in sequences 18🔒Pairs and the pigeonhole principle 13🔒Parity arrangements 6🔒Ramsey-type colourings 7🔒Smallest sums of sets 11🔒Subsets avoiding differences 13🔒
Graphs and networks83 problems · 7 skills
Counting graphs 10🔒Distances in lines and trees 14🔒Euler's formula 16🔒Networks and connections 7🔒Routes between cities 9🔒Spreading news 16🔒Trees and degrees 11🔒
Colourings and symmetry30 problems · 2 skills
Combinatorial geometry184 problems · 13 skills
Convex polygons and crossings 17🔒Counting triangles and shapes 9🔒Diagonals of a polygon 18🔒Dissections and cuts 13🔒Equidistant points and circles 14🔒Fractals 4🔒Intersections of chords and circles 16🔒Lattice points 18🔒Point sets 9🔒Regions from lines and cuts 17🔒Triangles from lines and points 17🔒Triangles in hexagons 16🔒Which lengths make a triangle 16🔒
Grids and chessboards121 problems · 9 skills
Chess pieces 18🔒Chessboard squares 15🔒Filling grids with rules 15🔒Grid colourings and partitions 17🔒Mazes and placement puzzles 5🔒Rectangles and lines on grids 16🔒Sign arrays and binary grids 10🔒Tables of sums and products 16🔒Tilings and colour patterns 9🔒