You need 27 tickets to guarantee a win on the UK National Lottery

In the UK National Lottery, players purchase tickets comprising their choices of six different numbers between 1 and 59. During the draw, six balls are randomly selected without replacement from a set numbered from 1 to 59. A prize is awarded to any player who matches at least two of the six drawn numbers. We identify 27 tickets that guarantee a prize, regardless of which of the 45,057,474 possible draws occurs. Moreover, we determine that 27 is the optimal number of tickets required, as achieving the same guarantee with 26 tickets is not possible.