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 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 AnswerYour 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 Answer