Question

suppose you see angry birds figures in the store. they have red, blue, yellow and gray birds, and also piggys. you want to get 3 matching matching figures, but you don't care which one. unfortunately, the figures are in packaging that doesn't allow you to see which figure you are getting before purchase. what is the minimum number of packages you need to buy in order to guarantee 3 matching figures?

Answer 1

Using the pigeonhole principle, you would need to buy a minimum of 9 packages to guarantee obtaining 3 matching Angry Birds figures.

Step-by-step explanation:

To guarantee getting 3 matching figures when picking from figures of red, blue, yellow, gray birds, and piggys, we can use the pigeonhole principle from mathematics. This principle states that if there are n pigeonholes and more than n pigeons, then at least one pigeonhole must contain more than one pigeon. Given that there are 5 types of figures, to ensure that we get 3 matching figures, we need to account for the possibility of getting a maximum of 2 of each type without getting a third matching one. Therefore, if we buy 2 each of the first 4 types (8 figures total) and then one more figure, we are guaranteed to get at least 3 figures of the same type. This is because the worst-case scenario would have us getting 2 reds, 2 blues, 2 yellows, 2 grays, and 1 piggy before getting a third matching figure. So the minimum number of packages needed to buy is 2(red) + 2(blue) + 2(yellow) + 2(gray) + 1 = 9 packages.