What is wrong with the following proof?
2=1
a = b
a2 = ab
a2 – b2 = ab – b2
(a+b)(a-b) = b(a-b)
a + b = b
2b = b
2 = 1
Hard Riddles
Two Water Lilies
Water lilies grow extremely rapidly. In one pond, a water lily grew so fast that each day it covered a surface area double that of the area it had covered the previous day. At the end of the 30th day, it had covered the pond entirely. How long do you think it will take for two such water lilies to cover the whole pond?
Riddle AnswerFill Pool with Water
A swimming pool has four taps. The first can fill the entire pool with water in two days, the second in three days, the third in four days, and the last one can fill the pool in 6 hours. How long will it take to fill the pool using all 4 taps together?
Riddle AnswerQuarter on the Table
Your friend pulls out a perfectly circular table and a sack of quarters, and proposes a game.
“We’ll take turns putting a quarter on the table,” he says. “Each quarter must lay flat on the table, and cannot sit on top of any other quarters. The last person to successfully put a quarter on the table wins.”
He gives you the choice to go first or second. What should you do, and what should your strategy be to win?
Riddle AnswerThree Friends
At school Joe has three friends: Tim, George and Paige. Two of them play football, two play tennis, and two play golf. The friend who doesn’t play golf doesn’t play tennis and the one who doesn’t play football doesn’t play golf. Paige doesn’t play tennis. Which sports does each person play?
Riddle Answer