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Question: How can you make the following true by adding a single line: .9 = 1.

Note: ≠ is not the answer.

Answer: .9 = 1.

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Question: You have an 8 by 8 chess board that has two corner squares diagonal from each other removed. Is there any way to place 31 dominoes of size 2x1 to cover the remaining 62 spaces?

Answer: No. When you remove the two diagonal spaces from the chess board they are both black or both white, making it so that there are two more of the other color. Each domino would cover 1 black and 1 white space. So 31 of them would have to cover 31 white spaces and 31 black spaces but with the corners removed there are 30 of one color and 32 of the other.

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3 coins (medium)

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Question: You have three coins. One always comes up heads, one always comes up tails, and one is just a regular coin (has equal change of heads or tails). If you pick one of the coins randomly and flip it twice and get heads twice, what is the chance of flipping heads again?

Answer: 90 percent. If you pick the heads coin the chance of getting the first 2 heads is 100 percent (4/4) and if you pick the fair coin the chance is 25 percent (1/4). So from this, the chance that it is the heads coin is 4/5 and the fair coin 1/5.

Then, if it is the heads coin you will definitely get heads (4/5). If you flip the fair coin it is 1/10 (1/5 * 1/2). Add the probabilities together: 4/5 + 1/10 = 9/10.

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Question: There are several different kinds, but the one you pick doesn't do its job.

What is it?

Answer: A lock.

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Riddle #1661 (medium)

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Question: A man challenges you to a coin flipping contest. One of you must flip heads, then tails, then heads. The other must flip heads, then tails, then tails. Whoever succeeds in fewer flips is the winner.

Which should you choose?

Answer: You should pick heads, tails, and tails. Both of them begin with heads then tails, giving you an equal chance of getting the first two. But if you have tails for the final flip and don't get it you are still 1/3 of the way through the sequence. If you have heads for the final flip and miss it you must start all over trying to get the sequence.

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