 |
| ||
| |||
|
| Math Central | Quandaries & 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? |
Gordon,
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.
Victoria
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.