Problem number 24. Each time a coin is put in the machine, a ball falls randomly from the bottom row. What is the smallest number of coins Sofia must have to be sure that she will get a white ball? To solve this problem, we should think about the worst case scenario, since that is the minimum number of coins Sofia needs to be 100% sure that she will get a white ball. Let's zoom in on the picture. In the worst case, we will get all of the balls before the white one in each column, like this. For example, in the first column, we should get the grey, black, and black balls. In the second, we will get a grey ball, and so on. If we get all 10 of these balls, this means that it's possible to put in 10 coins into the machine and not get a white ball. However, if we need to put another coin into the machine, notice that the bottom ball in each row is now a white ball. So now, we are mathematically guaranteed to get a white ball after 11 coins. Since 10 is the worst case, and this takes out all the balls that are not white at the bottom of the columns, now we will be 100% sure after inserting the 11th coin that we will get a white ball. That means that the answer is C, 11.

coin machine

white ball

worst case

guaranteed

11 coins