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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).
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 transformations of the 15 puzzle form a groupoid (not a group, as not all moves can be composed); [12] [13] [14] this groupoid acts on configurations.. 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]
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).
Automatic repeating of slides can be activated in windowed mode; Soft edge and glow effects are allowed in text frame objects; Objects can be centered on the slide (or page in Draw) in one step; Overflowing text in presenter notes is no longer cut off when printing; Draw. Support for clipping stroke paths in imported PDFs was added; Base
Image source: The Motley Fool. Pinterest (NYSE: PINS) Q4 2024 Earnings Call Feb 06, 2025, 4:30 p.m. ET. Contents: Prepared Remarks. Questions and Answers. Call ...
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
After such a file is created, typical operation is to present it as a slide show using a portable computer, where the presentation file is stored on the computer or available from a network, and the computer's screen shows a "presenter view" with current slide, next slide, speaker's notes for the current slide, and other information. [85]