It's the holidays and lots of people are traveling. Things are getting out of control at baggage claim. Suppose everybody has exactly one bag, tagged with their first and last initial, which are both uppercase letters from the English alphabet. What is the minimum number of people needed to guarantee that at least 3 luggage tags have the same 2 initials (in the same order) on them

Question

Mathematics

Daniel Benitez

3 September, 21:10

It's the holidays and lots of people are traveling. Things are getting out of control at baggage claim. Suppose everybody has exactly one bag, tagged with their first and last initial, which are both uppercase letters from the English alphabet. What is the minimum number of people needed to guarantee that at least 3 luggage tags have the same 2 initials (in the same order) on them

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Agustin · Answer 1

1353 people

Step-by-step explanation:

There are 26 letters in the English alphabet. Therefore there are 26*26 = 676 unique possible combinations there are for the baggage tagging. In the best case scenario, there are 676 different bags in which no bag have the same tagging initials on them. The 677th bag would have the same tagging initial on them as 1 of the previous 676 bag, making this the minimum number to guarantee 2 bags to have the same tagging initial.

Similarly, for the 3 bags to have the same tagging initials, the minimum number required would be 676*2 + 1 = 1353 bags or people