Answers for last week

1) Old Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent his remaining 8 years as an old man, how many years did he spend as an active man?

Let L = OMW's final age.

.25*L + .125*L + .5L + 8 = L

.875*L + 8 = L

8 = .125*L

64 = L

.5*L = Active man

.5*64 = 32 years

2) Mr. Brown has 8 black gloves and 8 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color?

He picks one, and it is of one color. The next one could either be a match or a different color though, so he needs to draw again. The third sock he pulls out will have to match one of the two previous ones pulled out. He only needs to draw three.

3) Last weekend, I went to play in the nearby park. It was really fun! I rode my new bicycle that Mom had given me for my birthday. On reaching the park, I saw that there was now a total of 20 bicycles and tricycles. If the total number of wheels was 50, how many tricycles were there?

(My personal favorite way of solving these is taking an extreme and working backwards from there.)

Assume all the vehicles were bikes. That means there were 20*2 = 40 wheels. We need 10 more wheels, and each time we swap one of the bikes for a trike, we add one wheel. Therefore we need to swap out 10 bikes. We end up with those 10 trikes and 10 (original 20 - swapped out 10) bikes.