"How Many Crayons Should He Grab?" Solution

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.

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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.