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Problem of the Week 1107

Strange Lottery

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Imagine a lottery where the winning number is abc, where letters are decimal digits and any or all of them can be 0. Thus there are 1000 possibilities for the winning number. But tickets for the lottery have only two digits, xy, and such a ticket wins if the winning number is xyA or Axy or xAy.

In short, having two digits in the right order wins. There are 100 possible tickets to buy.

How many tickets do you have to buy to guarantee a win?

Proof of optimality not required (though it can be done). One can do better than 100, since, for example, buying all tickets except 98 will win. The only possible missing ones are 98X, X98, and 9X8, and these are caught by 8X, X9, and X8, respectively.

Source: Math Horizons, Sept 2008, p. 33-34, by Tom Yuster.

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7 October 2008