The Coin Toss Riddle
You are in a bar having a drink with an old friend when he proposes a wager.
"Want to play a game?" he asks.
"Sure, why not?" you reply.
"Ok, here's how it works. You choose three possible outcomes of a coin toss, either HHH, TTT, HHT or whatever. I will do likewise. I will then start flipping the coin continuously until either one of our combinations comes up. The person whose combination comes up first is the winner. And to prove I'm not the cheating little weasel you're always making me out to be, I'll even let you go first so you have more combinations to choose from. So how about it? Is $10.00 a fair bet?"
You know that your friend is a skilled trickster and usually has a trick or two up his sleeve but maybe he's being honest this time. Maybe this is a fair bet. While you try and think of which combination is most likely to come up first, you suddenly hit upon a strategy which will be immensely beneficial to you. What is it?
"Want to play a game?" he asks.
"Sure, why not?" you reply.
"Ok, here's how it works. You choose three possible outcomes of a coin toss, either HHH, TTT, HHT or whatever. I will do likewise. I will then start flipping the coin continuously until either one of our combinations comes up. The person whose combination comes up first is the winner. And to prove I'm not the cheating little weasel you're always making me out to be, I'll even let you go first so you have more combinations to choose from. So how about it? Is $10.00 a fair bet?"
You know that your friend is a skilled trickster and usually has a trick or two up his sleeve but maybe he's being honest this time. Maybe this is a fair bet. While you try and think of which combination is most likely to come up first, you suddenly hit upon a strategy which will be immensely beneficial to you. What is it?
Hint: Think what would be most likely to happen if you chose HHH, would this be a good decision?
The answer is to let your friend go first. This puzzle is based on an old game/scam called Penny Ante. No matter what you picked, your friend would be able to come up with a combination which would be more likely to beat yours. For example, if you were to choose HHH, then unless HHH was the first combination to come up you would eventually lose since as soon as a Tails came up, the combination THH would inevitably come up before HHH. The basic formula you can use for working out which combination you should choose is as follows. Simply take his combination (eg. HHT) take the last term in his combination, put it at the front (in this case making THH) and your combination will be more likely to come up first. Try it on your friends! Did you answer this riddle correctly?
YES NO
YES NO
Russian Roulette Riddle
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Hint:
Russian Roulette
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Answer
Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:
1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Therefore player 2 has an 4/6 or 2/3 chance of winning. Did you answer this riddle correctly?
YES NO
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Answer
Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:
1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Therefore player 2 has an 4/6 or 2/3 chance of winning. Did you answer this riddle correctly?
YES NO
Old Man On London Bridge
I met an old man on London bridge,
As the sun set on the ridge,
He tipped his hat and drew his name,
And cheated at the guessing game.
What was the mans name?
As the sun set on the ridge,
He tipped his hat and drew his name,
And cheated at the guessing game.
What was the mans name?
Hint:
Andrew. In the third line, and drew his name. It works better when you say it. Did you answer this riddle correctly?
YES NO
YES NO
Cinderella Playing Soccer
Hint:
Polar Bear Dice Riddle
Polar bears around an ice hole, like petals around a rose. The game is in the name, and the name is in the game. How many polar bears are there?" Johnny asked as he rolled the five dice. The first roll produced 4, 6, 1, 3, 2. "Six," said Billy. "No, two," Johnny replied. The next roll was 5, 1, 5, 2, 4. "Four?" said Billy. "No, eight," Johnny said. The next rolls were 3, 5, 3, 1, 2. There were 8 polar bears. The next rolls were 6, 2, 1, 2, 4. There were no polar bears. How does Johnny figure out the number of polar bears?
Hint: A rose by any other name...could be a die?
Dice all look the same. On a die, the 1, 3, and 5 all have a dot in the center. The 3 has 2 dots on either side of the center dot, and the 5 has 4 dots around the center dot. Johnny simply counted the number of dots around the outside. A "3" has 2 "petals around the rose, or polar bears around an ice hole." The "5" has 4 "petals" or "polar bears." Roll some dice and it will become clear!! Did you answer this riddle correctly?
YES NO
YES NO
With Eyes That See I Cant Be Found Riddle
Hint:
Prisoner Hat Riddle
There is a wall between prisoners C and D (which cannot be seen through or around). Prisoner A can see prisoners B and C (by moving his head to the side). Prisoner B can see prisoner C. Prisoners C and D see only the wall.
The prisoners are immobilized in the ground and can't twist their body to see the person behind them. The warden shows them two black hats and two white hats and then puts the hats in a bag to conceal them. He then stands behind each prisoner, chooses a hat from the bag, and puts it on their head. The color of each prisoner's hat is shown in the image above.
The rules are simple. If any prisoner can figure out the color of the hat on his head, all four prisoners will be set free. But they must be sure, if one of them simply guesses and is wrong, they will all be shot dead! The prisoners are not allowed to talk to each other and they have 10 seconds.
The warden counts down "ten, nine, eight, seven". All four prisoners are silent. The warden smiles, knowing that he put the hats on in such a way that no prisoner could possibly know the color of the hat they had on. He continues "six, five, four, thr.."
"I know the color of my hat!" one of the prisoners finally blurts out.
Which prisoner called out and why is he 100% certain of the color of his hat?
Hint:
Prisoner B.
If prisoners B and C had the same color hat on, prisoner A would have know immediately that his hat was the other color (there are only two hats of each color). Since prisoner A was silent, prisoners B and C must have different colored hats. Prisoner B realized this and knew that his hat was not the same color as prisoner C, therefore his hat must be black! Did you answer this riddle correctly?
YES NO
If prisoners B and C had the same color hat on, prisoner A would have know immediately that his hat was the other color (there are only two hats of each color). Since prisoner A was silent, prisoners B and C must have different colored hats. Prisoner B realized this and knew that his hat was not the same color as prisoner C, therefore his hat must be black! Did you answer this riddle correctly?
YES NO
Add Your Riddle Here
Have some tricky riddles of your own? Leave them below for our users to try and solve.