Brainteaser Puzzles | Mind Teaser | Math Logic

## Sep 28, 2007

### The Cheating Runners (logic Brainteaser Puzzles)

When Alex, Brian and Chris finished their race they were feeling very tired. It had been raining very heavily, so heavily in fact that the judges were unable to see who came in first, who second and who third. When he asked the three men, they each made two statements. One man lied in both his statements. The other two told the truth. This is what they said:

Alex said, ‘I came in first, Chris was last.’

Brian said, ’Alex wasn’t first. Chris came in second.’

Chris said, ‘I was before Alex. Brian wasn’t second.’

So what was the order in which they crossed the finishing line?

Clue for the Puzzle: What Alex and Brian say about Chris disagrees. Therefore one of them must be lying.

Answer for the Puzzle: Alex and Brian say different things about Chris. Therefore one of them is lying and Chris must be telling the truth. Since Chris says he was before Alex, it is obvious that Alex is lying about coming first. Therefore the real order must have been Brian (who wasn’t second, according to Chris who told the truth), then Chris (Because Brian said so, and he also was telling the truth)-finally Alex.

### The Local Bus (Math Brainteaser puzzles)

The local minibus that runs from our village to the nearest town has the following seating regulations:

Maximum Capacity:

Sitting: 8 adults or 12 children

Standing: 2 adults or 4 children

As the last bus drew up at one of the stops on Saturday evening there were six adults who wanted to get on. But there were already seven children in the bus. How many of the adults would be able to get on the bus if the regulations were observed?

Clue for the Puzzle: If 12 children can sit in the same space as eight adults, how much room would three children take up?

Answer for the Puzzle: No problem! If 12 children can sit in the same space as eight adults then three children could sit in the same space for two adults. This meant that if four children stood up and three remained seated, there would still be room for the six adults to sit down. So everyone was able to get on.

## Sep 25, 2007

### Predicting the Color (Logic Brainteaser Puzzle)

There are three boxes labeled ‘red balls’, ‘White balls’ and ‘red and white balls’. Each of the labels is incorrect. You are allowed to take one ball only from each box. How can you label each box correctly?

(Of course, you are not allowed to look inside!)

Clue for the Puzzle:

It will be sufficient to correctly identify one box. We know that all the boxes are incorrectly labeled. Once one box has been correctly identified, all we need to do is to switch the labels on the other two boxes.

The first thing to do is to take a ball from the box incorrectly labeled ‘red and white balls’. If it is red, then clearly this is the box containing red balls. If white, then white. Since we know that the boxes are all incorrectly labeled it is now sufficient to switch the two remaining labels.

### Job Interview (Logic Brainteaser Puzzle)

An employer was very anxious to find the most intelligent of the three men who had applied for a job. So he told them: ‘here are five conical hats. Three are white and two are black. I shall place a hat on each of your heads. When you turn around, you will be able to see the others’ hats but not your own. The first one to tell me the color of his own hat will get the job.’ He then placed a white hat on each man’s head. When the three men turned to face each other there was a long silence. Then, suddenly, one of the candidates said, ‘Mine is white.’

How did he know?

Clue for the Puzzle:

There are three possible combinations: two men had black hats and one a white one (this must be excluded because if one man had seen two black hats, he would immediately have known his was white); two had white hats and one had a black one; all three had white hats.

The secret is to work out the color of one’s own hat from what the other people must able to see.

He could see two white hats. Therefore he might have had on either a white or a black hat. He then reasoned like this: Suppose my hat is black. If it is, my two rivals A and B can each see a black hat and a white hat. One of them (A) might then work out that his own hat could not be black because, if it were, B would see two black hats and would know that his own hat must therefore be white. B says nothing however. A might therefore conclude, if my hat is black, then his own hat must be white. But since he does not come to this conclusion, then my assumption that my hat is black must be false. Therefore my hat must be white.

## Sep 18, 2007

### Ali the Thief (Survival Brainteaser Puzzle)

Ali the thief had managed to break into the Sultan’s treasure room. He was looking for a bag containing 1250 diamonds, each weighing 0.8 grams. Unfortunately, the Sultan had filled nine other bags with imitation diamonds. There were 1000 in each bag, each one weighing 1 gram. So all 10 bags weighed exactly 1000 grams and all the bags looked exactly alike. Just as Ali was scratching his head, the Sultan burst in with his guards. As he was a merciful Sultan, he gave Ali a chance to save his life. Here is what he said; “If you can find the bag which contains the real diamonds by using these scales just once, you may keep the diamonds. If not, you will be beheaded. You can take stones from any of the bags and put them in other bags if you wish but you can only weigh once!”

How did Ali save his neck?

Clue for the Puzzle:

Suppose there were only three bags. If Ali took one stone from bag no. 1, two from bag no. 2, and three from bag no. 3 and weighed them together, would he be able to tell which the bag of diamonds was?

Ali put the bags in a row and removed one stone from the first bag, two from the second, three from the third, etc. He therefore had 55 stones. If all the stones weighed 1 gram, the total weight would be 55 grams. But Ali knew that some were 0.2 grams lighter. So supposing the total weight had been 54.6 grams, he would have known that it was bag no.2 which contained the diamonds (53 stones at 1 gram and two stones at 0.8 gram each = 1.6 grams). If the total had weighed 54.2 grams, he would have known it was the fourth bag he was looking for (51 stones at 1 gram and 4 stones at 0.8 gram each = 3.2 grams). In this way he could locate the bag with the real diamonds with no trouble at all.

### No place like Vegas (Gambling Brainteaser Puzzle)

Las Vegas is the place for gambling in America. I was just coming out of a Casino when a man came up to me and said “I’ll bet you \$5 that if you give me \$10, I’ll give you \$15.” What do you think I did?

Clue for the Puzzle:

What would be the result if he lost the bet?

I told him to go and look for another fool to try it on! If I had accepted his bet and given him the \$10, he would simply have said “I lose the bet.” He would then have given me the \$5 he had bet me. But I would have lost the other \$5 through my stupidity.

### Two men (Tricky Brainteaser Puzzle)

Two men were standing facing in opposite directions. Yet each one could see the other without turning around. How was that possible?

Clue for the Puzzle:

Which way were they looking if they could see each other?

They were facing each other.

### Indians Family (Logic Brainteaser Puzzle)

Two Indians were talking to each other about their family relationships. The fat one said to the thin one, “Your father is my father’s son.” “That’s right.” replied the thin one, “and you yourself have neither sons nor brothers.” How were the two Indians related?

The thin one was the daughter of the fat father.

### Dividing Cows (Math Brainteaser Puzzle)

When farmer Jones died he left a herd of 17 cows. In his will he gave instructions that the cows were to be divided as follows: ½ to his eldest son, Sam, 1/3 to his second son, Michael, and 1/9 to his youngest son, Benjamin. The three brothers could not see how this was possible. Luckily for them, a passing professor of mathematics heard of this problem and solved it for them. How?

Clue for the Puzzle:

Suppose there had been 18 cows, how many each would the sons have got?

The professor of mathematics suggested they add one imaginary cow before doing their division:

½ of 18 = 9

1/3 of 18 = 6

1/9 of 18 = 2

Total = 9+6+2 = 17

Curiously enough, as you can see, this adds up to 17!

### Jealous Men (Classic Brainteaser Puzzle)

Three men with their wives come to a river. The boat they find can only take 2 people at a time. Because the men are all extremely jealous, no woman can be left with another man unless her own husband is also present. So how do they manage to cross the river?

Clue for the Puzzle:

Start off by A taking his wife across and coming back alone.

A takes his wife across and return alone. Then B’s and C’s wife cross together. A’s wife comes back. B and C then cross over and B comes back with his wife, leaving C and his wife on the far side. A and B then cross and C’s wife returns. A’s and B’s wives now cross. C rows back and fetches his wife.

### Amoebas (Math Brainteaser Puzzle)

Amoebas are a very simple form of life and are able to reproduce very quickly. It only takes three minutes for an amoeba to reproduce itself. In the laboratory there were two jars of equal size. In one of them there were two amoebas. It took them 3 hours to fill the jar. As an experiment, I placed one amoeba in the second jar. How long did it take to fill the jar?

Clue for the Puzzle:

After 3 minutes, there are two amoebas in the second jar too.

It takes 3 hours and 3 minutes for the second jar to be filled.

### Gangsters’ game (Survival Brainteaser Puzzle)

The gangsters have captured a rival. They intend to kill him but in order to make it more interesting, their leader says to him: “make any statement you like. If it’s true, you’ll be hanged. If it is false, you’ll be shot.” What does the man say that saves him?

Clue for the Puzzle:

He must find something which is true if it is false, and false if it is true.

He says ‘I will be shot’ If this is true then he will be hanged, but he cannot be hanged because he cannot then be shot, and it would not then be true, and he could not therefore be hanged…

### The Troubled Chef (Logic Brainteaser Puzzle)

The famous chef Henri Labouffe had a problem. His staff had broken some of the kitchen crockery. He had a jug full of vinegar but he only needed 4 deciliters. His only measuring jars were for 5 deciliters and 3 deciliters. So how did he manage to measure 4, without wasting any vinegar?

Clue for the Puzzle:

Start by filling the 5 deciliter container. Then fill the 3 deciliter container. This leaves 2 deciliters in the 5 deciliters container. Then pour the 3 deciliters back into the jug.

Then pour the 2 deciliters into the 3 deciliters container. Refill the 5 deciliters container. Pour 1 deciliter into the 3 deciliter container, thus filling it. 4 deciliters are left in the 5 deciliter container.

### The Relationships (Logic Brainteaser Puzzle)

A woman pointed to the photograph of a man and said to her father, ‘That man’s mother was my mother’s mother in law.” What was the relationship between the woman and the man in the photograph?”

Clue for the Puzzle:

Who was her mother married to?

The woman was either the man’s daughter or his niece.

### Cigarette Man (Logic Brainteaser Puzzle)

Harry has the habit of picking up cigarette ends left by other people. He knows that he can make one new cigarette out of seven ends. One Saturday night he collected 49 cigarettes ends. The next day he made them into cigarettes and smoked them all.

How many whole cigarettes did he smoke that day?

Clue for the Puzzle:

Do not forget that the cigarettes he has made will also produce cigarettes ends.

## Sep 14, 2007

### Cats in the Room (Logic Brainteaser Puzzle)

In a square room there was a cat in each corner, three cats in front of each cat and a cat on each cat’s tail. How many cats were there altogether?

Clue for the Puzzle:

How many corners are there to a room?

There were four cats.

### Tongue Twisters (Language Brainteaser Puzzle)

Can you say these tongue-twisters quickly?

1. The cricket critic cricked his neck at a critical cricket match.

2. There are thirty thousand feathers on that thrush’s throat.

3. Please, Paul, pause for applause.

4. How many cookies could a good cook cook if a good cook could cook cookies?

### Four Errors (Language Brainteaser Puzzle)

There is four errers in this centence. Can you find them?

1. There are

2. errors

3. sentence

4. The fourth error is the fact that there are only 3 errors in the sentence

### Riddles (Brainteaser Puzzle)

1. What has four legs and a back but cannot walk or move on its own?

2. What touches you all the time without being seen?

3. What can smile and move and laugh, just like you, without being alive?

4. What has a mouth bigger than its head?

5. What is always coming but never arrives?

6. What can’t you say without breaking it?

7. Why is an empty room like a room full of married people?

8. Why do birds fly south?

9. How long will a seven day clock run without winding?

10. What has four legs and flies?

11. What is the difference between a flea and an elephant?

1. A chair

2. The air

3. Your picture in the mirror

4. A river

5. Tomorrow

6. The word ‘silence’

7. Because there isn’t a single person

8. Because walking would take too long

9. It won’t run

11. An elephant can have fleas, but a flea can’t have elephants.

### Discovering People’s Age (Math Brainteaser Puzzle)

Here is a mind-reading trick which will enable you to discover a person’s age. Ask a friend to:

multiply his age by 2

multiply the result by 50

add the age of his father

subtract the number of days in a year

When he/she gives you the result, you will tell him his age and that of his father.

How to do it: Add 115 to the number you get. The first two numbers will represent your friend’s age, the last two is his father’s age.

multiply it by 5