配置や計画に際し起こる諸問題に数学的解決を与えようとする組合せ論には3000年の歴史があります。並べ替えと組合せに始まり、グラフ理論や集合の分割、ブロック計画、コード設計、ラテン方陣などに発展していきました。特定の場所で止まるという条件を満たす最短経路を求めたり、隣接国には違う色を使用するなどの条件で最少の色数で地図を塗るには何色必要か、などを考えつつ、組合せ論とその応用を概括します。
　　

• Introduces Combinatorics through a problem-solving approach
• Covers the core aspects of the subject such as permutations, combinations, and latin squares
• Explores a variety of classic and modern problems, from the Könisberg bridges to Sudoku puzzles

 
How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal)
  
Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.