NSML Assumed Knowledge

Last updated: 2021-11-28

These facts will be assumed without any further commentary on contests and problems.

  • All random selection is fair unless stated otherwise. (See below for details.)
  • Cards
    • A standard deck of 52 cards has 13 ranks and 4 suits each.
    • Ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
    • Suits: clubs, hearts, diamonds, spades.
    • Note: the two jokers found in some decks of cards will never be considered.
    • Vocabulary: draw or deal from a deck.
  • Dice
    • A standard n-sided die has possible outcomes {1,2, …, n}.
    • Vocabulary: die (singular) and dice (plural) are rolled.
    • A fair die is one in which all outcomes are equally likely.
  • Coins
    • A standard coin has two outcomes: Heads and Tails.
    • Vocabulary: a coin is flipped or tossed.
    • A fair coin is one in which the probability of each outcome is 1/2.
  • Letters
    • There are 26 letters in the standard alphabet.
    • Vocabulary
      • Vowels are A, E, I, O, and U.
      • Consonants are all 21 other letters, including Y.
      • Word means any string of letters.
  • Fairness
    • Every possible outcome is equally likely.
    • Unless a problem explicitly explains selection is unfair, fair choice should be assumed.