# Logic Puzzles

What are some of your favorite logic puzzles? For example, one that was told to me yesterday was:

You are looking at a dish with a cell in it. It takes one minute for the cell to divide in half. If the dish is completely full in 30 minutes, how long does it take for the dish to be half full?
If no one gets the answer I’ll post it later. Does anyone else have any?

There is a bridge four people need to cross, bu they only have seventeen minutes to do it in. Here’s the problem, though: it is pitch black and there is only one flashlight. Also, the bridge is such that only two people can cross at a time.

The four people take different times to cross; they are: 1 minute, 2 minutes, 5 minutes, and 10 minutes.

As an example: person 1 and person 10 go across with the flashlight. This takes 10 minutes (since 10 is so darned slow!). Person 1 carries the flashlight back to the other side. 11 minutes now. Person one and five go across, taking 5 minutes, making a total of 16. 1 heads back, 17 minutes is up!

Though the solution to this is online, it isn’t impossible to figure out and there’s no juggling flashlights or standing halfway on the bridge to guide people across. Everyone crosses two at a time one way, and a return trip to get the next person.

Answer to SwimmingithChickens’ question: 29 minutes.

Erislover’s: 1 and 2 cross first. (2 min)
1 comes back. (1 min)
5 and 10 cross. (10 min)
2 comes back. (2 min)
1 and 2 cross. (2 min)

SwC: 29 minutes.

eris:
1 and 2 go, 1 comes back. (3 minutes)
10 and 5 go, 2 comes back. (12 + 3 = 15)
1 and 2 go. (15 + 2 = 17).

It would take

29 minutes for the dish to be half-full

Fenris

One of my favorites that drives people nuts (I got it from a Piers Anthony book):

There are twelve coins and a balance scale before you. One of the coins is counterfeit, but you do not know which. You do know that the counterfeit coin is a different weight from the other coins, but you do not know if it is lighter or heavier, only that it is different.

In three weighings, find the counterfeit.

(remember, you have to be able to cover all contingencies)

Yep 29 minutes. Good one eris! Also Max has me quite intrigued… Any other good logic puzzles out there?

Mr. Jones walked outside during a pouring rain for 20 minutes without getting a single hair on his head wet. He didn’t wear a hat, carry an umbrella, or hold anything over his head. His clothes got soaked.

How could this happen?

1. Twenty metal blocks are of the same size and external appearance; some are aluminium and the rest are duraluminium, which is heavier. Using at most eleven weighings on a pan balance, determine how many blocks are aluminimum.

2. Three married couples on a journey come to a river where they find a little skiff, which can hold at most two people. The husbands are very jealous and no husband will leave his wife without him in company where another man is present. How can all three couples cross the river.

3. Three thieves rob a merchant of a vase containing 24 ounces of balsam and three empty vessels of volume 13, 11 and 5 ounces respectively. How can they divide their booty equally?

Ike: The man has no head. Or something.

Mr. Jones is bald.

God, you guys are morbid. Try again.

Thank you, fatmac98.

Jabba, I got # 2 and # 3

1. Two random wives cross. Two random husbands cross. The remaining husband and wife crosses.

3.) Fill the 13 volume vessel. Drain 5 ounces into the 5 ounce vessel. You are left with 8 ounces. Do this twice.

Mr. Jones lives on the 12th floor of his apartment building in Schenectady. Whenever he gets into the automatic elevator on the ground floor, and no one else is in the elevator, he pushes the button for the 6th floor, gets off on the 6th floor, and walks up the stairway to the 12th floor. He would much prefer to ride the elevator all the way up to his own floor.

Why does he do this?

because the elevator only goes up to the sixth floor?

SwC, problems with both of those.

1. How does the boat get back each time?
2. Where do you put the third portion of 8oz? In a 5oz. container?

Uke: Being the headless horseman, he has to carry his head in his arms all the time. As such, he can’t reach all the way up to the 12 floor button. He likes it when it rains, because he then gets to carry his umbrella around, and can use that to hit the 12 button.

SWC:2) Once the 2 wives have crossed how does the boat get back for the 2 husbands to cross?
3) After you’ve done it once, where are you putting the 5 ounces so you can do it the second time?

Sorry, they weren’t that easy.

IkeThere are armed gunmen waiting for him on the 12th floor.

Mr. Jones is bald.

Ok, I rushed into things… that damn 12 coin scale question is still eating up my active memory. I think I still can answer #2 though.

The 2 wives cross, one comes back, crosses with the last wife. comes back. Then two husbands go. one back, two more go, one comes back. The key is that the last couple has to be married to each other.