What does the following represent?
N N N N N N N
A A A A A A A
C C C C C C C
7 up cans.logic
Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. All three competitors know one another's shooting odds. If you are Mr. Black, where should you shoot first for the highest chance of survival?
He should shoot at the ground. If Mr. Black shoots the ground, it is Mr. Gray's turn. Mr. Gray would rather shoot at Mr. White than Mr. Black, because he is better. If Mr. Gray kills Mr. White, it is just Mr. Black and Mr. Gray left, giving Mr. Black a fair chance of winning. If Mr. Gray does not kill Mr. White, it is Mr. White's turn. He would rather shoot at Mr. Gray and will definitely kill him. Even though it is now Mr. Black against Mr. White, Mr. Black has a better chance of winning than before.logic
There is a barrel with no lid and some wine in it. "This barrel of wine is more than half full," said Curly. Moe says, "No it's not. It's less than half full."
Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?
Tilt the barrel until the wine barely touches the lip of the barrel. If the bottom of the barrel is visible then it is less than half full. If the barrel bottom is still completely covered by the wine, then it is more than half full.logicmath
Using only and all the numbers 3, 3, 7, 7, along with the arithmetic operations +,-,*, and /, can you come up with a calculation that gives the number 24? No decimal points allowed.
[For example, to get the number 14, we could do 3 * (7 - (7 / 3))]
7 * ((3 / 7) + 3) = 24logicshort
A boat has a ladder that has six rungs, each rung is one foot apart. The bottom rung is one foot from the water. The tide rises at 12 inches every 15 minutes. High tide peaks in one hour. When the tide is at it's highest, how many rungs are under water?
None, the boat rises with the tide. logic
This teaser is based on a weird but true story from a few years ago. A complaint was received by the president of a major car company: "This is the fourth time I have written you, and I don't blame you for not answering me because I must sound crazy, but it is a fact that we have a tradition in our family of having ice cream for dessert after dinner each night. Every night after we've eaten, the family votes on which flavor of ice cream we should have and I drive down to the store to get it. I recently purchased a new Pantsmobile from your company and since then my trips to the store have created a problem. You see, every time I buy vanilla ice cream my car won't start. If I get any other kind of ice cream the car starts just fine. I want you to know I'm serious about this question, no matter how silly it sounds: 'What is there about a Pantsmobile that makes it not start when I get vanilla ice cream, and easy to start whenever I get any other kind?'" The Pantsmobile company President was understandably skeptical about the letter, but he sent an engineer to check it out anyway. He had arranged to meet the man just after dinner time, so the two hopped into the car and drove to the grocery store. The man bought vanilla ice cream that night and, sure enough, after they came back to the car it wouldn't start for several minutes. The engineer returned for three more nights. The first night, the man got chocolate. The car started right away. The second night, he got strawberry and again the car started right up. The third night he bought vanilla and the car failed to start. There was a logical reason why the man's car wouldn't start when he bought vanilla ice cream. What was it?
HINT: The man lived in an extremely hot city, and this took place during the summer. Also, the layout of the grocery store was such that it took the man less time to buy vanilla ice cream.
Vanilla ice cream was the most popular flavor and was on display in a little case near the express check out, while the other flavors were in the back of the store and took more time to select and check out. This mattered because the man's car was experiencing vapor lock, which is excess heat boiling the fuel in the fuel line and the resulting air bubbles blocking the flow of fuel until the car has enough time to cool.. When the car was running there was enough pressure to move the bubbles along, but not when the car was trying to start.
How many times can you subtract 5 from 25?
Just once, because after you subtract anything from it, it's not 25 anymore.logicmathprobability
You are on a gameshow and the host shows you three doors. Behind one door is a suitcase with $1 million in it, and behind the other two doors are sacks of coal. The host tells you to choose a door, and that the prize behind that door will be yours to keep.
You point to one of the three doors. The host says, "Before we open the door you pointed to, I am going to open one of the other doors." He points to one of the other doors, and it swings open, revealing a sack of coal behind it.
"Now I will give you a choice," the host tells you. "You can either stick with the door you originally chose, or you can choose to switch to the other unopened door."
Should you switch doors, stick with your original choice, or does it not matter?
You should switch doors.
There are 3 possibilities for the first door you picked:
You picked the first wrong door - so if you switch, you win
You picked the other wrong door - again, if you switch, you win
You picked the correct door - if you switch, you lose
Each of these cases are equally likely. So if you switch, there is a 2/3 chance that you will win (because there is a 2/3 chance that you are in one of the first two cases listed above), and a 1/3 chance you'll lose. So switching is a good idea.
Another way to look at this is to imagine that you're on a similar game show, except with 100 doors. 99 of those doors have coal behind them, 1 has the money. The host tells you to pick a door, and you point to one, knowing almost certainly that you did not pick the correct one (there's only a 1 in 100 chance). Then the host opens 98 other doors, leave only the door you picked and one other door closed. We know that the host was forced to leave the door with money behind it closed, so it is almost definitely the door we did not pick initially, and we would be wise to switch.logicmystery
A couple went on holiday for three weeks. They carefully locked their house, and had a neighbor check on the place while they were gone. When they returned, the wife was distressed to lean that because of a power failure she had lost all her fine jewelry. She had hidden the jewelry in what she thought was a very safe place. She was not robbed. Her jewelry was lost by accident. Why?
In this true incident, the wife had hidden her best jewelry inside her freezer in a bag among all the frozen food. Because of a general power failure the freezer had gone off. A friendly neighbour (who had a key in order to water the plants) had tried to be helpful by throwing out all the bad food - and with it went the jewelry. logicmath
Consider the following explanation for why 1=2:
1. Start out Let y = x
2. Multiply through by x xy = x2
3. Subtract y2 from each side xy - y2 = x2 - y2
4. Factor each side y(x-y) = (x+y)(x-y)
5. Divide both sides by (x-y) y = x+y
6. Divide both sides by y y/y = x/y + y/y
7. And so... 1 = x/y + 1
8. Since x=y, x/y = 1 1 = 1 + 1
8. And so... 1 = 2
How is this possible?
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not followinng basic mathematical rules, we are able to get strange results like these.