Please help me understand this question. I got the answer 101, however it says the solution to this question is 11. Perhaps it was a typo?
Suppose you select some items from a box that contains fifty items, where there are ten each of the colors blue, red, green, yellow, and purple. How many items must you select to make sure that you get at least three of the same color?
As requested, I will express the problem and my thoughts. Note that ceiling division is used in this problem. I will denote ceiling division with the symbols [x], and I will use <= for less than or equal to.
3 <= [X/50]
2 < X/50
100 < X
101 <= X
This is how my discrete structures professor requested how I complete this problem.
Think of the bins, one for each color. Keep putting the marbles in the binary color. If we got two for each color, that would be 5 * 2 = 10 marbles. The next marble,regarldess of color, would make one of the bins contain 3 marbles. Yes by chance we could use fewer marbles, but 11 is the worst case scenario.
This is the essence of the pigeonhole principle. The bins are the pigeonholes and, we see how we can fill the pigeonholes without the condition holding. Then we add one more object to obtain the solution.