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In general, if G is the number of gold pieces and N (> 2G) is the number of pirates, then All pirates whose number is less than or equal to 2G + M will survive, where M is the highest power of 2 that does not exceed N – 2G. Any pirates whose number exceeds 2G + M will die. Any pirate whose number is greater than 2G + M/2 will receive no gold.
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Therefore, a game of value ∗, which is a first-player win, is neither positive nor negative. However, ∗ is not the only possible value for a first-player win game (see nimbers ). Star does have the property that the sum ∗ + ∗ , has value 0, because the first-player's only move is to the game ∗, which the second-player will win.
Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively.
The rational number / is unknown, and the goal of the problem is to recover it from the given information. In order for the problem to be solvable, it is necessary to assume that the modulus m {\displaystyle m} is sufficiently large relative to r {\displaystyle r} and s {\displaystyle s} .
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