Math CentralQuandaries & Queries


Question from Gordon:

There are 50 numbers in a Lottery Draw and 5 numbers are drawn out. The player chooses 5 numbers can you tell what is the lowest number of entries required to guarantee that 3 of the 5 numbers entered match 3 of the 5 numbers drawn?


There are 50 choose 3 = 19,600 different triples of numbers from among 1, 2, ..., 50. There are 5 choose 3 = 10 triples of numbers on each ticket. Thus, at least 1960 tickets are required. I think it is possible to prove that, in this case, there is no collection of 1960 tickets that does the job. In that case I doubt that the actual minimum number of tickets is known. Problems like this are remarkably difficult.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS