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  2. 15 puzzle - Wikipedia

    en.wikipedia.org/wiki/15_puzzle

    [2] [3] For the 15 puzzle, lengths of optimal solutions range from 0 to 80 single-tile moves (there are 17 configurations requiring 80 moves) [4] [5] or 43 multi-tile moves; [6] the 8 Puzzle always can be solved in no more than 31 single-tile moves or 24 multi-tile moves (integer sequence A087725). The multi-tile metric counts subsequent moves ...

  3. The monkey and the coconuts - Wikipedia

    en.wikipedia.org/wiki/The_monkey_and_the_coconuts

    n 5 n 4 n 3 4 4 0 s 4 s 3 s 2 4 4 4 1 But the same reasoning again applies to N' as applied to N, so the next digit of N' is 4, so s 2 and n 3 are also 4, etc. There are 5 divisions; the first four must leave an odd number base 5 in the pile for the next division, but the last division must leave an even number base 5 so the morning division ...

  4. Sudoku solving algorithms - Wikipedia

    en.wikipedia.org/wiki/Sudoku_solving_algorithms

    A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. [1] Players and investigators use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties.

  5. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    The period of ⁠ c / k ⁠, for c coprime to k, equals the period of ⁠ 1 / k ⁠. If k = 2 a ·5 b n where n > 1 and n is not divisible by 2 or 5, then the length of the transient of ⁠ 1 / k ⁠ is max(a, b), and the period equals r, where r is the multiplicative order of 10 mod n, that is the smallest integer such that 10 r ≡ 1 (mod n).

  6. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    Alice: Task 1 = 1, Task 2 = 2. George: Task 1 = 5, Task 2 = 8. The greedy algorithm would assign Task 1 to Alice and Task 2 to George, for a total cost of 9; but the reverse assignment has a total cost of 7. Fortunately, there are many algorithms for finding the optimal assignment in time polynomial in n.

  7. Mortgage rates stay flat as Trump’s second term comes into ...

    www.aol.com/finance/mortgage-rates-stay-flat...

    Average 15-year mortgage rates followed the same pattern, hitting 5.99% this week versus 6% a week earlier. 10-year Treasury yields, which are closely linked to mortgage rates, moved higher ...

  8. Unit fraction - Wikipedia

    en.wikipedia.org/wiki/Unit_fraction

    Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n.It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number.

  9. College Football Playoff matchups, bracket, schedule revealed ...

    www.aol.com/college-football-playoff-matchups...

    No. 5 Texas vs. No. 12 Clemson. Saturday, Dec. 21 at 4 p.m. ET on TNT and Max. Darrel K Royal Texas Memorial Stadium, Austin, Texas. Winner to play No. 4 Arizona State in quarterfinals.

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