marbles come in 10 different varieties and there are 15 marbles in a pack.how many packs must a person buy in order to be sure of having at least 10 of one kind?
Hmm. cool question.
Let's say there are 10 marbles per bag. The most bags you'd need to buy would be 10. If there were one of each color in the bag, then you couldn't guarantee 10 of a color unless you had 10 bags. If any bag had a surplus of one color, you'd need fewer bags to get 10 of that color, unless another bag were lacking that color.
Now, what if there are 11 marbles per bag? After 8 bags, you'd have 88 marbles, so you could have 8 of each color, with 8 colors having 9 marbles. Add a 9th bag, and you have 99 marbles, meaning that at least one of the colors would have 10 representatives.
Let's jump to 15 marbles per bag. After 6 bags you have 90 marbles, so you might have only 9 of each color. Add a 7th bag and some color has to reach the 10 mark.