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The goal is to arrange the squares into a 4 by 6 grid so that when two squares share an edge, the common edge is the same color in both squares. In 1964, a supercomputer was used to produce 12,261 solutions to the basic version of the MacMahon Squares puzzle, with a runtime of about 40 hours.
A puzzle about the two-cube calendar was described in Gardner's column in Scientific American. [1] [2] In the puzzle discussed in Mathematical Circus (1992), two visible faces of one cube have digits 1 and 2 on them, and three visible faces of another cube have digits 3, 4, 5 on them. The cubes are arranged so that their front faces indicate ...
Using this technique for all rows and columns at the start of the puzzle produces a good head start into completing it. Note: Some rows/columns won't yield any results initially. For example, a row of 20 cells with a clue of 1 4 2 5 will yield 1 + 1 + 4 + 1 + 2 + 1 + 5 = 15. 20 - 15 = 5. None of the clues are greater than 5.
The below birth colors were developed by astrologer and numerologist Michele Bernhardt, who matched each birth month with a Pantone color. And you can read more in her book Colorstrology: What ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Proof without words that all centered octagonal numbers are odd squares. Squares of even numbers are even, and are divisible by 4, since (2n) 2 = 4n 2. Squares of odd numbers are odd, and are congruent to 1 modulo 8, since (2n + 1) 2 = 4n(n + 1) + 1, and n(n + 1) is always even. In other words, all odd square numbers have a remainder of 1 when ...
It is NP-complete to solve Nurikabe, even when the involved numbers are 1 and 2 only. Further, consider these two rules of Nurikabe: Black cells form a connected area; Black cells cannot form 2 × 2 squares, Either one can be ignored, giving a total of three variants. As it turns out, they are all NP-complete. [2]
The numbers are based on a $50 a square game, with a $625 payout for the 1st and 3rd quarters, a $1,250 payout for halftime, and a $2,500 payout for the end of the game. (The cells are colored ...