# Logic Puzzles

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1. The Camels

Four tasmanian camels traveling on a very narrow ledge encounter four tasmanian camels coming the other way.

As everyone knows, tasmanian camels never go backwards, especially when on a precarious ledge. The camels will climb over each other, but only if there is a camel sized space on the other side.

The camels didn't see each other until there was only exactly one camel's width between the two groups.

How can all camels pass, allowing both groups to go on their way, without any camel reversing?

Hint: Use match sticks or coins to simulate the puzzle.

Solution: First a camel from one side moves forward, then two camels from the other side move forward, then three camels from the first side move forward etc...

etc...

2. The Waiter

Three men in a cafe order a meal the total cost of which is \$15. They each contribute \$5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return \$5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the \$5 between the three he simply gives them \$1 each and pockets the remaining \$2 for himself.

Now, each of the men effectively paid \$4, the total paid is therefore \$12. Add the \$2 in the waiters pocket and this comes to \$14.....where has the other \$1 gone from the original \$15?

Solution: The payments should equal the receipts. It does not make sense to add what was paid by the men (\$12) to what was received from that payment by the waiter (\$2)

Although the initial bill was \$15 dollars, one of the five dollar notes gets changed into five ones. The total the three men ultimately paid is \$12, as they get three ones back. So from the \$12 the men paid, the owner receives \$10 and the waiter receives the \$2 difference. \$15 - \$3 = \$10 + \$2.

3. The Boxes

There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

How can you label the boxes correctly?

Solution:

Pick from the one labeled "Apples & Oranges". This box must contain either only apples or only oranges.

E.g. if you find an Orange, label the box Orange, then change the Oranges box to Apples, and the Apples box to "Apples & Oranges."

4. The Cannibals

Three cannibals and three anthropologists have to cross a river.

The boat they have is only big enough for two people. The cannibals will do as requested, even if they are on the other side of the river, with one exception. If at any point in time there are more cannibals on one side of the river than anthropologists, the cannibals will eat them.

What plan can the anthropologists use for crossing the river so they don't get eaten?

Note: One anthropologist can not control two cannibals on land, nor can one anthropologist on land control two cannibals on the boat if they are all on the same side of the river. This means an anthropologist will not survive being rowed across the river by a cannibal if there is one cannibal on the other side.

Solution:

First, two cannibals go across to the other side of the river, then the rower gets called back. Next, the rowing cannibal takes the second across and then gets called back, so now there are two cannibals on the far side.

Two anthropologists go over, then one anthropologist accompanies one cannibal back, so now there is one anthropologist and one cannibal on the far side.

The last two anthropologists go over to the far side, so now all the anthropologists are across the other side, along with the boat and one cannibal.

In two trips, the cannibal on the far side takes the boat and ferries the other two cannibals across the river.

5. The Father

A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.

Where's the father?

Solution: With the mother. If you do the math, you find out the child will be born in 9 months.

6. The Double Jeopardy Doors

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.

There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.

You can, however, ask one robot one question. The problem is one robot always tells the truth ,the other always lies and you don't know which is which.

What is the question you ask?

Hint: The two robots know each others personality. That they talk when they're bored, lonely, etc. Try to get the two robots to cancel their evil & good ways out.

Solution: Ask one robot what the other robot would say, if it was asked which door was safe. Then go through the other door.

7. The Frog

A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.

Hint: Try to think the problem through for a five meter well. Now what is the solution for the 30 meter well?

Solution: 28

Each day he makes it up another meter, and then on the twenty seventh day he can leap three meters and climb out.

8. The Bobber

You can paddle your canoe seven miles per hour through any placid lake. The stream flows at three miles per hour. The moment you start to paddle up stream a fisherman looses one of his bobbers in the water fourteen miles up stream of you.

How many hours does it take for you and the bobber to meet?

Hint: Assume the stream moves at a perfectly constant three miles an hour.

Solution: 2

Ignore the speed of the stream, as the cork will be carried along at three miles per hour as will you. It takes two hours to travel fourteen miles, at a rate of seven miles per hour.

9. The Socks

Cathy has twelve black socks and twelve white socks in her drawer.

In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?

Solution: 3

Socks do not come in in left and right, so any black will pair with any other black and any white will pair with any other white. If you have three socks and they are either colored black or white, then you will have at least two socks of the same color, giving you one matching pair.

10. There is something about Mary

Mary's mum has four children.
The first child is called April.
The second May.
The third June.
What is the name of the fourth child?

Solution: Mary.

Mary's mothers fourth child was Mary herself.

11. Petals around the rose

The name of the game is Petals Around the Rose, and that name is significant. Newcomers to the game can be told that much. They can also be told that every answer is zero or an even number. They can also be told the answer for every throw of the dice that are used in the game. And that's all the information they get.

The person who has the dice and knows the game, rolls five dice and remarks almost instantly on the answer. For example: in Roll #1 the answer is two.

Roll #1.

"The answer is what?" says the new player.

"Two."

"On that roll?"

"Yes."

"Would it still be two if I moved the dice without turning any of them over, just rearranging the pattern?"

"I can tell you only three things: the name of the game, the fact that the answer is always even, and the answer for any particular throw. In this case the answer is two."

"So that's how it is. What am I supposed to do?"

"You're supposed to tell me the answer before I tell you. I'll give you all the time you want, but don't tell me your theory, just the answer. If you figure it out, you don't want to give the idea away to these other jokers around you. Make them work for the answers, too. If you get the answer right on six successive rolls, I'll take that as prima facie evidence that you understand the game."

"OK, roll again."

Roll #2.

"I give up. What's the answer?"

"Roll again."

Roll #3.

Roll #4.