What is wrong with the following proof?

2=1

a = b

a^{2} = ab

a^{2} – b^{2} = ab – b^{2}

(a+b)(a-b) = b(a-b)

a + b = b

2b = b

2 = 1

What is wrong with the following proof?

2=1

a = b

a^{2} = ab

a^{2} – b^{2} = ab – b^{2}

(a+b)(a-b) = b(a-b)

a + b = b

2b = b

2 = 1

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 AnswerA 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 AnswerIf it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?

Riddle Answer