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The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem [1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
In game theory, " guess 2 3 of the average " is a game that explores how a player’s strategic reasoning process takes into account the mental process of others in the game. [1] In this game, players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player (s) who select a number closest to ...
Monty Hall problem. In search of a new car, the player chooses a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let ...
The Pillai sequence tracks the numbers requiring the largest number of primes in their greedy representations. [30] Similar problems to Goldbach's conjecture exist in which primes are replaced by other particular sets of numbers, such as the squares: It was proven by Lagrange that every positive integer is the sum of four squares.
100 prisoners problem. Each prisoner has to find their own number in one of 100 drawers, but may open only 50 of the drawers. The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive.
Bernard: Of course we know the bus number, but we still don't know your age. Cheryl: Oh, I forgot to tell you that my brothers have the same age. Albert and Bernard: Oh, now we know your age. So what is Cheryl's age? [13] Note that this problem is a slight variation of another problem, previously presented by Martin Gardner. [14]
The birthday problem in this more generic sense applies to hash functions: the expected number of N-bit hashes that can be generated before getting a collision is not 2 N, but rather only 2 N ⁄ 2. This is exploited by birthday attacks on cryptographic hash functions and is the reason why a small number of collisions in a hash table are, for ...
Induction puzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction. [ 1][ 2] A puzzle's scenario always involves multiple players with the same reasoning capability, who go through the same reasoning steps. According to the principle of induction, a solution to the ...