The Math Profs

Chalkboard

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.
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December 2020
## Categories## AuthorsBrian 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. |

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