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The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines.
Typically, it is assumed that w ≥ log 2 (max(n, K)); that is, that machine words are large enough to represent an index into the sequence of input data, and also large enough to represent a single key. [2] Integer sorting algorithms are usually designed to work in either the pointer machine or random access machine models of computing. The ...
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
The number of possible positions of the 24 puzzle is 25! / 2 ≈ 7.76 × 10 24, which is too many to calculate God's number feasibly using brute-force methods. In 2011, lower bounds of 152 single-tile moves or 41 multi-tile moves had been established, as well as upper bounds of 208 single-tile moves or 109 multi-tile moves.
In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use fewer comparisons.
In mathematics, the amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That is, s ( a )= b and s ( b )= a , where s ( n )=σ( n )- n is equal to the sum of positive divisors of n except n itself (see also divisor function ).
Of the primes occurring in this decomposition, 2, 5, and 7, only 7 is congruent to 3 modulo 4. Its exponent in the decomposition, 2, is even. Therefore, the theorem states that it is expressible as the sum of two squares. Indeed, 2450 = 7 2 + 49 2. The prime decomposition of the number 3430 is 2 · 5 · 7 3. This time, the exponent of 7 in the ...
Bubble/Shell sort: Exchange two adjacent elements if they are out of order. Repeat until array is sorted. Insertion sort: Scan successive elements for an out-of-order item, then insert the item in the proper place. Selection sort: Find the smallest (or biggest) element in the array, and put it in the proper place. Swap it with the value in the ...
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