“As we grow up, we learn that even the one person that wasn’t supposed to ever let us down, probably will. You’ll have your heart broken and you’ll break others’ hearts. You’ll fight with your best friend and you’ll cry because time is flying by. So take too many pictures, laugh too much, forgive freely, and love like you’ve never been hurt. Life comes with no guarantees, no time outs, no second chances. You just have to live life to the fullest, tell someone what they mean to you and tell someone off, speak out, dance in the pouring rain, hold someone’s hand, comfort a friend, fall asleep watching the sun come up, stay up late, be a flirt, and smile until your face hurts. Don’t be afraid to take chances or fall in love and most of all, live in the moment.”—
How many mathematicians does it take to screw in a light bulb?
If k mathematicians can change a light bulb and if one more simply watches them do it, then k+1 mathematicians will have changed the lightbulb. Therefore, by induction, for all n in the positive integers, n mathematicians can change a light bulb.
A rope over the top of a fence has the same length on each side and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkeys mother. The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey plus the weight of the banana is one-fourth the sum of the weights of the rope and the weight. The monkeys mother is one half as old as the monkey will be when it is three times as old as its mother was when she was one half as old as the monkey will be when it is as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was one third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was one fourth as old as it is now. How long is the banana?