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A variant of the story has been told with 11 camels, to be divided into 1 ⁄ 2, 1 ⁄ 4, and 1 ⁄ 6. [22] [23] Another variant of the puzzle appears in the book The Man Who Counted, a mathematical puzzle book originally published in Portuguese by Júlio César de Mello e Souza in 1938. This version starts with 35 camels, to be divided in the ...
For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...
The monkey and the coconuts is the best known representative of a class of puzzle problems requiring integer solutions structured as recursive division or fractionating of some discretely divisible quantity, with or without remainders, and a final division into some number of equal parts, possibly with a remainder.
Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems.
Three types of pictures (or frames) are used in video compression: I, P, and B frames. An I‑frame ( Intra-coded picture) is a complete image, like a JPG or BMP image file. A P‑frame (Predicted picture) holds only the changes in the image from a previous frame. For example, in a scene where a car moves across a stationary background, only ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
The Tower of Hanoi (also called The problem of Benares Temple[ 1] or Tower of Brahma or Lucas' Tower[ 2] and sometimes pluralized as Towers, or simply pyramid puzzle[ 3]) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on ...
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