Question

A major fast-food chain held a contest to promote sales. With each purchase, a customer was given a card with a whole number less than 100 on it. A $100 cash prize was given to any person who presented cards whose numbers totaled 100. The following are several typical cards. Can you find a winning combination? 3 9 12 15 18 27 51 72 84. Can you suggest how the contest could be structured so that there would be at most 1000 winners throughout the country?

Answer 1

A winning combination for the fast-food chain contest cards totaling 100 is 72 + 15 + 12 + 1. To have at most 1000 winners, the contest could limit high-value cards or implement traceable card numbers and issuance limits.

Step-by-step explanation:

To find a winning combination of cards that total 100 from the given numbers 3, 9, 12, 15, 18, 27, 51, 72, 84, one approach is to look for subsets that add up to 100. After some trial and error, we can see that 72 + 15 + 12 + 1 equals 100, which is a winning combination.

To structure the contest so that there would be at most 1000 winners nationwide, the fast-food chain could limit the number of certain high-value cards or have unique card numbers that are traceable and limit the issuance of winning combinations. Another approach could be to have a larger selection of numbers or specific rules that make it mathematically improbable to have more than 1000 unique winning combinations.