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A restated version of Selvin's problem appeared in Marilyn vos Savant's Ask Marilyn question-and-answer column of Parade in September 1990. [3] Though Savant gave the correct answer that switching would win two-thirds of the time, she estimates the magazine received 10,000 letters including close to 1,000 signed by PhDs, many on letterheads of ...
Like all other complete bipartite graphs, it is a well-covered graph, meaning that every maximal independent set has the same size. In this graph, the only two maximal independent sets are the two sides of the bipartition, and are of equal sizes. , is one of only seven 3-regular 3-connected well-covered graphs. [26]
[3] [4] They are usually issued once every week or two weeks, and due one or two weeks later. [ 4 ] [ 5 ] If used as part of a summative assessment they are usually given a low weight , [ 6 ] between 10% and 25% of the total mark of the course for all problem sets put together, [ 3 ] [ 5 ] and sometimes will count for nothing if the student ...
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.
Equivalently, this is the smallest set that could be produced by a greedy algorithm that tries to solve the no-three-in-line problem by placing points one at a time until it gets stuck. [3] If only axis-parallel and diagonal lines are considered, then every such set has at least n − 1 {\displaystyle n-1} points. [ 18 ]
The Parker square, named after recreational mathematician Matt Parker, [55] is an attempt to create a 3 × 3 magic square of squares — a prized unsolved problem since Euler. [56] The Parker square is a trivial semimagic square since it uses some numbers more than once, and the diagonal 23 2 + 37 2 + 47 2 sums to 4107 , not 3051 as for all the ...
The American Invitational Mathematics Examination (AIME) is a selective and prestigious 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics examination (formerly known as the AHSME), and starting in 2010, those who rank in the top 2.5% on the AMC 10.
For example, an exact cover problem is equivalent to an exact hitting set problem, an incidence matrix, or a bipartite graph. In computer science, the exact cover problem is a decision problem to determine if an exact cover exists. The exact cover problem is NP-complete [3] and is one of Karp's 21 NP-complete problems. [4]