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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.
Andersson et al. (1998) provide a randomized algorithm called signature sort that allows for linear time sorting of sets of up to 2 O((log w) 1/2 − ε) items at a time, for any constant ε > 0. As in the algorithm of Kirkpatrick and Reisch, they perform range reduction using a representation of the keys as numbers in base b for a careful ...
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters.
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 decomposition is 3, an odd number. So 3430 cannot be written as the sum of two squares.
Digits 1 and 2 need to be placed on both cubes to allow numbers 11 and 22. That leaves us with 4 sides of each cube (total of 8) for another 8 digits. However, digit 0 needs to be combined with all other digits, so it also needs to be placed on both cubes. That means we need to place remaining 7 digits (from 3 to 9) on the remaining 6 sides of ...
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.
alternate the direction such that one radial has smallest number at the outside, the adjacent radial has largest number outside. Each group occupies the radial position corresponding to the number on the Luoshu magic square, i.e., group 1 at 1 position, group 2 at 2 position etc. Finally arrange center group at the center circle, such that ...
People are given n unit squares and have to pack them into the smallest possible container, where the container type varies: Packing squares in a square: Optimal solutions have been proven for n from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any square integer. The wasted space is asymptotically O(a 3/5).
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