Question 1: The correct answer is 4 crayons. If Jeremy picks 2 crayons, they might be the same color. Might. But, then again, they might not. And Jeremy wants a guarantee, so 2 crayons won't cut it.
What about 3?
Nope. He might end up with only one of each color.
Will 4 crayons do it? Why, yes! It will! Even in the worst case scenario, where the first 3 crayons are each a different color, the 4th crayon would have to match one of the first 3 crayons since there are only 3 distinct colors.
Question 2: The correct answer is 21 crayons. If Jeremy picks 20 crayons, then it's technically possible for him to have 13 blues, 6 browns, and 1 red. So 20 crayons is still not enough to guarantee at least 2 reds. He would need to grab 21 crayons for the guarantee.
Question 3: The correct answer is 35 crayons. If Jeremy picks up 34 crayons, he might have all reds and blues. He would need one more to guarantee he has at least 1 crayon of each color.
Question 4: The correct answer is 26 crayons. The first 19 crayons Jeremy grabs could be all blues and browns. In this (unlucky) case, he would have 6 browns and would need to grab 7 more crayons from the box, which now contains only the red crayons.
And if you still want more puzzles of a similar type, check out our "How Many Socks?" book, for sale at our store www.themathprofs.com. We'll walk you through the process of solving these types of questions - from questions just like these, slowly building to more general scenarios using variables for the numbers of colors and items.
Brian and Melanie Fulton both earned doctoral degrees in mathematics at Virginia Tech. They formerly taught math at the university level, and now run a hobby farm while accuracy-checking collegiate mathematics texts. They homeschool their four children, frequently employing the aid of chicken, dairy goat, cat, and dog tutors.