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This page contains numbers appearing in combinatorics, which don’t fit on other lists.

List of numbers appearing in combinatorics Edit

  • In the Gregorian calendar, there are 217 combinations of day of the week and day in the month, Friday the 13th being the most (in)famous.
  • Article 79 of the Basic Law for the Federal Republic of Germany requires constitutional amendments to be approved by an absolute two-thirds majority of the Bundestag along with a simple two-thirds majority of the Bundesrat. Article 51 of the same law gives each state at least three votes, a fourth vote for states with more than 2 million inhabitants, a fifth vote for states with more than 6 million inhabitants, and a sixth vote for states with more than 7 million inhabitants. There are currently four states with three votes, seven states with four votes, one state with five votes, and four states with six votes. A calculation reveals that of the 65,536 possible voting patterns, 7,228 lead to an absolute two-thirds majority.
  • The number 7,825 is the smallest natural number n for which the set {1, 2, 3, … , n} cannot be written as a union of two disjoint sets, such that both of them contain no Pythagorean triples.[1]
  • The Kubo character has 11,007 possible mouth expressions and 4,429 possible brow expressions, and therefore 11,007×4,429 = 48,750,003 possible facial expressions.

Sudoku-related numbers Edit

  • 405 is the sum of all the numbers on a 9×9 Sudoku grid. It is equal to 9×T9, where Tn is the nth triangular number. This number is also called Ternary-dust mite.
  • 6,670,903,752,021,072,936,960 is a combinatoric number equal to the number of possible 9×9 Sudoku grids.[2]
  • 109,110,688,415,571,316,480,344,899,355,894,085,582,848,000,000,000 is the product of all the numbers on a 9×9 Sudoku grid. It is equal to 19×29×39×49×59×69×79×89×99, the product of the first 9 9th powers.

Sources Edit

  1. Boolean Pythagorean triples problem
  2. Mathematics of Sudoku - Wikipedia