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
Walk to Factory
A father and son work in the same factory. The father takes 30 minutes to walk to his factory and the son is able to cover the same distance in only 20 minutes. If the father were to leave the house 5 minutes earlier, how soon would his son catch up with his father?
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 AnswerTwo 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 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