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 Answer100 Apples in 5 Days
A man ate 100 apples in the past five days. Each day he ate 6 more apples than the previous day. How many did he eat on the 4th day?
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 Answer