In mathematical combinatorics, the Transylvania lottery is a lottery where players selected three numbers from 1-14 for each ticket, and then three numbers are chosen randomly. A ticket wins if two of the numbers match the random ones. The problem asks how many tickets the player must buy in order to be certain of winning.
(Javier Martínez, Gloria Gutiérrez & Pablo Cordero et al. 2008, p.85)(Mazur 2010, p.280 problem 15)
An upper bound can be given using the Fano plane with a collection of 14 tickets in two sets of seven. Each set of seven uses every line of a Fano plane, labelled with the numbers 1 to 7, and 8 to 14.
Low set
1-2-5
1-3-6
1-4-7
2-3-7
2-4-6
3-4-5
5-6-7
High set
8-9-12
8-10-13
8-11-14
9-10-14
9-11-13
10-11-12
12-13-14
At least two of the three randomly chosen numbers must be in one Fano plane set, and any two points on a Fano plane are on a line, so there will be a ticket in the collection containing those two numbers. There is a (6/13)*(5/12)=5/26 chance that all three randomly chosen numbers are in the same Fano plane set. In this case, there is a 1/5 chance that they are on a line, and hence all three numbers are on one ticket, otherwise each of the three pairs are on three different tickets.
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also contributed music to the soundtrack of the animated film Hotel Transylvania 2, performing their song "I'm in Love with a Monster". They released...
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Sycamore Shoals, more popularly referred to as the Transylvania Purchase (after Henderson's Transylvania Company, which had raised money for the endeavor)...
"Nelvana Announces MIPTV Highlights". "Nelvana, Sony partner on Hotel Transylvania TV series". Milligan, Mercedes (June 9, 2015). "Nelvana Assembles Partners...
(1993) Pebbles (1994–1995) Colgate (1994) Esso (1995) Pepsi (1995) Virginia Lottery (1995) Apple Macintosh (1995) National Highway Traffic Safety Administration...
the U.S. state of North Carolina include the North Carolina Education Lottery, three Indian casinos, charitable bingo and raffles, and low-stakes "beach...
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