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According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).
Because the combinations of the 15 puzzle can be generated by 3-cycles, it can be proved that the 15 puzzle can be represented by the alternating group. [15] In fact, any 2 k − 1 {\\displaystyle 2k-1} sliding puzzle with square tiles of equal size can be represented by A 2 k − 1 {\\displaystyle A_{2k-1}} .
The rearrangement inequality can be regarded as intuitive in the following way. Imagine there is a heap of $10 bills, a heap of $20 bills and one more heap of $100 bills. You are allowed to take 7 bills from a heap of your choice and then the heap disappears.
The slide (Schleifer in German, Coulé in French, Superjectio in Latin) [1] is a musical ornament often found in baroque musical works, but used during many different periods. [1] It instructs the performer to begin two or three scale steps below the marked note and "slide" upward—that is, move stepwise diatonically between the initial and ...
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a ...
Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip (which can usually be pulled out, flipped over and reinserted for convenience), still others on one side only ("simplex" rules).
The goal is to construct m triplets, each of which contains one element from A, one from B and one from C, such that the sum of each triplet is T. [ 2 ] The 4-partition problem is a variant in which S contains n = 4 m integers, the sum of all integers is m T {\displaystyle mT} , and the goal is to partition it into m quadruplets, all ...
It can also convert back and forth between the 2010 and the 2007 formats. [21] Microsoft has documented the OneNote file format. It is an open format that can store varied multimedia content in a single .one file. [18] [22] [23] Multiple .one files can be exported to a .onepkg file, which stores multiple .one files (corresponding to the ...