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 A328950 Numerators for the "Minimum-Redundancy Code" card problem. 0
 0, 3, 9, 19, 33, 51, 74, 102, 135, 173, 216, 264, 318, 378, 444, 516, 594, 678, 768, 864, 966, 1074, 1188, 1308, 1435, 1569, 1710, 1858, 2013, 2175, 2344, 2520, 2703, 2893, 3090, 3294, 3505, 3723, 3948, 4180, 4419, 4665, 4918, 5178, 5445, 5719, 6000, 6288, 6584, 6888, 7200, 7520, 7848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Given a deck of cards consisting of one 1, two 2's, three 3's, ..., n n's, what's the best average number of yes-or-no questions needed to ask to determine a randomly drawn card?  The answer is the above sequence divided by the number of cards (A000217). The problem can be solved using Huffman codes. This problem was popularized in Martin Gardner's Scientific American "Mathematical Games" column, and was included in his book "My Best Mathematical and Logic Puzzles". REFERENCES Gardner, M. (1995). My best mathematical and logic puzzles. New York: Dover Publications Inc, p29, puzzle #52 "Playing Twenty Questions when Probability Values Are Known" LINKS D. A. Huffman, A Method for the Construction of Minimum-Redundancy Codes, in Proceedings of the IRE, vol. 40, no. 9, pp. 1098-1101, Sept. 1952. EXAMPLE For n=2, there are 3 cards, so a(2)/3 = 3/3 = 1 question is needed on average. For n=3, there are 6 cards, so a(3)/6 = 9/6 = 1.5 questions are needed on average. CROSSREFS Cf. A286496. Sequence in context: A226184 A066506 A058331 * A049749 A147055 A146638 Adjacent sequences:  A328947 A328948 A328949 * A328951 A328952 A328953 KEYWORD nonn,frac AUTHOR Danny Pflughoeft, Nov 10 2019 STATUS approved

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Last modified February 21 23:00 EST 2020. Contains 332113 sequences. (Running on oeis4.)