### Brain Teasers

# Flip a Coin

A man makes the following proposition to his friend:

"I will let you flip a coin 20 times. Each time the coin lands on heads, I will give you $2.00. However, each time the coin lands on tails, you must give me $3.00."

His friend flips the coin 20 times and the end result is that no money is to change hands.

How many times did the coin land on heads?

"I will let you flip a coin 20 times. Each time the coin lands on heads, I will give you $2.00. However, each time the coin lands on tails, you must give me $3.00."

His friend flips the coin 20 times and the end result is that no money is to change hands.

How many times did the coin land on heads?

### Answer

Since each won and lost an equal amount, the following equation can be used to find the solution: 2x = 3(20-x), where x = number of times heads came up.Solving this results in 5x = 60. Thus, x = 12.

The coin must have landed on heads a total of 12 times in order for no money to exchange hands.

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