Brainteaser Puzzles

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.

Answer for the Puzzle:

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.

Answer for the Puzzle:

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.

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?

Answer for the Puzzle:

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?

Answer for the Puzzle:

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.