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# Puzzles to tease you

1. It was a sunny beautiful morning. The air was fresh and a mild wind was blowing against my windscreen. I was traveling from point A to point B. It took me 1 hour and 30 minutes to complete the journey.

After lunch I returned to point A. I drove for 90 minutes. How do you explain it?

2. Recently I attended a cocktail party. There was a beautiful young woman, who also seemed very witty and intelligent. One of the other guests suddenly popped a question at her "How old are you?" For a moment she looked a bit embarrassed and while I stood there wondering how she was going to wriggle out of the situation, she flashed a charming smile and answered, "My age three years hence multiplied by 3 and from that subtracted three times my age three years ago will give you my exact age.

The man who asked her the age just walked away puzzled. Then she leaned over and whispered to me "if he can calculate that one, he deserves to know my age."

How old do you think she is?

3. It was a Christmas day. A day to exchange gifts. Two fathers gave their sons some money. One father gave his son 150$ and the other 100$. But when the two sons counted their money, they found that between them they had become richer by only 150$.

How do you explain this?

4. It was a Christmas day. And on this day we decided that my whole family should meet. The gathering consisted of one grand-father, one grand mother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. We were altogether seven.

How do you explain it?

5. The following problem is supposed to have been given by Euclid in his lectures in Alexandria about 280 B.C.

A mule and a donkey were going to the market laden with wheat. The mule said"if you give me one measure, I should carry twice as much as you, but if I give you one, we should have equal burdens.

What were their burdens?

6. We have a brick of regular size. It weighs 4 kilogrammes. How much do you think a similar brick, four times smaller, but made of the same material weigh?

7. If 6 men can pack 6 packets of candy in 6 minutes how many men are required to pack 60 packets in 60 minutes?

8. In my neighborhood lives a man who weighs 200 pounds. He has two sons. They both weigh 100 pounds each. On a festival day they decide to go across the river on a boat to visit some relations. But the boat could carry a maximum load of only 200 pounds.

Yet they managed to get across the river. How did they do it?

9. We have 100 ft piece of ribbon.

If it takes one second to cut it into a 1 foot strip how long would it take to cut the entire ribbon into one foot strips?

10. 1,3,6,10

Name the next three numbers in the series.

## Solutions

1. There is nothing to explain here. the driving time there and back is absolutely the same because 90 minutes and 1 hour and 30 minutes are one and the same thing. This problem is meant for inattentive readers who may think that there is some difference between 90 minutes and 1 hour 30 minutes.

2. This problem can be solved by the application of algebra. Suppose if we take x for the years, the age three years hence will be x+3 and the age three years ago x-3.

Now the equation is 3(x+3)-3(x-3)=x. When we solve it we get x=18. The girl is 18 years old.

To check this: three years hence she will be 21 and three years ago she was 15. And the difference is: (3*21)-(3*15) = 63-45 = 18

3. One of the fathers is the son of the other father. The problem posed would seem as if there are altogether four persons concerned. But there are only three. The three persons are grandfather, father and son. The grandfather gave his son 150$ and the latter passed on 100$ of them to the grandson (i.e his son). Thus increasing his own money by 50$.

4. There were two girls and a boy, their father and mother, and their father's father and mother.

As it would be too much for words to go into the explanations of relationships here, the most satisfactory thing for you to do would be to sit down, write out a list of the seven people involved, and check off the twenty three relationships.

5. The burdens were 7 and 5.

6. One would quickly come out with the answer, 1 kilogram, that is four times less. But this is wrong.

The smaller brick is not only four times shorter than the real one, but it is also four times shorter than the real one, but it is also four times narrower and four times lower and therefore its volume and weight are 4*4*4 = 64 times.

The correct answer would be 4000:64 = 62.5 grammes.

7. 6 men pack 6 boxes in 6 minutes; 6 men pack 1 box in 1 minute; 6 men pack 60 boxes in 60 minutes.

8. First the two sons rowed across the river and one stayed behind while the other returned in the boat to his father. The son remained behind while the father crossed the river. Then the other son brought back the boat and the two brothers rowed over together.

9. One minute and thirty nine seconds, because when the ninety ninth cut is made, the remaining foot does not have to be cut.

10. 15, 21, 28. These are triangular numbers: 1, 3, 6, 10, 15, 21, 28 .... n(n+1)/2.

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## Comments

6 is ambiguous. Does it mean in length or in volume?