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A187353
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Number of possible ways to fill out NCAA Division I Men's Basketball Tournament Office Pool by year, 1939-2011.
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1
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128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 32768, 32768, 2097152, 8388608, 8388608, 16777216, 4194304, 8388608, 4194304, 16777216, 8388608, 16777216, 16777216, 16777216, 4194304, 2097152, 4194304, 4194304, 16777216, 16777216, 16777216
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1939,1
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COMMENTS
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The number a(n) is 2^(k-1) where k is the number of teams in the tournament in year n. The sequence includes any play-in games in preliminary rounds but does not include regional or national third place games.
The number of teams year by year is as follows (source: Wikipedia, detailed list in the b-file):
1939-1950: eight teams; 1951-1952: 16 teams; 1953-1974: varied between 22 and 25 teams; 1975-1978: 32 teams; 1979: 40 teams; 1980-1982: 48 teams; 1983: 52 teams (four play-in games before the tournament); 1984: 53 teams (five play-in games before the tournament); 1985-2000: 64 teams; 2001-2010: 65 teams (with an opening round game to determine whether the 64th or 65th team plays in the first round); 2011-future: 68 teams (four play-in games before the tournament, the nominal first round).
An office pool is where people try to predict the outcome of every single NCAA Tournament game before it starts. The probability of doing so perfectly by randomly choosing is 1/a(n).
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LINKS
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Wikipedia, NCAA Men's Division I Basketball Championship for the number of teams year-by-year, as well as the articles on individual tournaments between 1953-1974 as those do not have specific numbers listed on the main page.
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FORMULA
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a(n) = 2^(k-1) where k = number of teams in the NCAA Tournament of year n.
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EXAMPLE
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a(1939) = 2^(8-1) = 2^7 = 128 since there were 8 teams in the 1939 NCAA Tournament.
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CROSSREFS
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KEYWORD
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dumb,easy,fini,full,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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