Solution

Solutions to the puzzles

1. The first brother is 70 inches tall, the second 72 the third 74 and the fourth brother 80 inches tall.

2. Twenty-six minutes.

3. Since the boys have as many brothers as sisters, there must be 1 boy more than the number of girls. If we try 2 and 1, 3 and 2, and 4 and 3, we will find that 4 boys and 3 girls is the solution to fulfill the requirement that each girl has twice as many brothers as sisters.


4. Naturally, the train travelling against the spin of the earth. This train will wear its wheels out more quickly, because the centrifugal force is less on this train.

5. No, the answer is not 32§ miles an hour, though this figure is the obvious answer! However, this represents the average of the 2 speeds and not the average speed for the whole trip.
If the time is equal to the distance divided by the average speed, then the time for the trip starting
from San Francisco equals s/40 and the time for the s return trip is is » which gives us a total time of 40 which equals "MO •
Therefore the average speed for the whole trip when the average speed equals the distance 1SS divided by the time is 2S divided by ~soo which, „_ . 200 , . , , 400S „„ 10 equals 2S times iss% which equals i3s~or 30— ~f3.

6. The lowest square number I can think of, contain-ing all the nine digits once and only once, is 139854276, the square of 11826, and the highest square number under the. same conditions is 932187456 the square of 30384.

7. Here is the formula that gives the minutes past twelve to which the hour hand points when the minute hand is exactly thirty minutes ahead.

30
Minutes past twelve Y=—[ (n—1) 2+11 where n is the next hour— Let's take the case of at what time between 4 and 5 will the hands be opposite each other? (n= 5).
30 270 . _, 6
.-.Y = -pp x 9 = "TP* 24tt. i.e. the hour hand will be 24 TT minutes past 4. The formula may be derived from the following: If X is distance moved by the minute hand Y is the distance moved by hour hand

then X—Y = 30 First time the hands move round X = 12 Y Second time the hands move round X = 12 Y—5 Third time the hands move round X = 12 Y—10 etc.

8. While striking 7 the clock strikes its first gong at 7 o'clock and it strikes 6 more at regular intervals. These 6 intervals take 7 seconds so that the intervals between gongs is 7/6 seconds. However to
strike 10 there are 9 intervals each taking (7/6)*9  seconds for a total of 10.5 seconds.

9. In order that the little girl should have disposed of the oranges she had remaining after her second sale, she; must have had at least one whole orange remaining so that she could deduct from it 'half of her oranges plus half an orange', for the third and the final sale. Therefore, if 1 orange represents half of the remaining after the second sale, then she must have sold two oranges in her second sale, leaving the 3 oranges after the first sale.
Lastly if three oranges only represent half the original number, plus half an orange, then she must have started with [ (3x2)+1] or 7 oranges.


10. The minimum number of weights required is five and these should weight 1, 3, 9, 27 and 81
pounds. 

Puzzles to puzzle you

Interesting Puzzles

"We cannot solve our problems with the same

 thinking we used when we created them."

                                                                                                                 - Albert Einstein

1. 

TALL MEN NEXT DOOR

Next door to me live four brothers of different heights. Their average height is 74 inches, and the difference in height among the first three men is two inches/'The difference between the third and the fourth man is six inches.

Can you tell how tall is each brother?

2. A MATTER OF TIME

Fifty minutes ago if it was four times as many minutes past three o'clock, how many minutes is it until six o'clock?

3. 

BROTHERS AND SISTERS

A family I know has several children. Each boy in this family has as many sisters as brothers but each of the girls has twice as many brothers as sisters. How many brothers and sisters are there?

4. AROUND THE EQUATOR

Two identical trains, at the equator start travelling round the world in opposite directions. They start together, run at the same speed and are on different tracks.

Which train will wear out its wheel treads first?

5. OVER THE GOLDEN GATE

While in San Francisco some time back, I hired a car to drive over the Golden Gate bridge. 1 started in the  afternoon when there was no traffic rush. So I could do 40 miles an hour. While returning, however, I got caught in the traffic rush and I could only manage to drive at a speed of 25 miles an hour.

What was my average speed for the round trip?

6. THE DIGITS AND SQUARE NUMBERS

All the nine digits are arranged here so as to form four square numbers:

9, 81, 324, 576

How would you put them together so as to form a single smallest possible square number and a single largest possible square number?

7. THE HOUR HAND AND THE MINUTE HAND

We all know that the hour hand and the minute hand on a clock travel at different speeds. However there are certain occasions when the hands are exactly opposite each other. Can you give a simple formula for calculating the times of these occasions?

8. 

THE GONG

Supposing a clock takes 7 seconds to strike 7, how long does it take for the same clock to strike 10?

9. SOMETHING FOR THE MARMALADE

A little girl I know sells oranges from door to door.

One day while on her rounds she sold i an orange more than half her oranges to the first customer. To the second customer she sold i an orange more than half of the remainder and to the third and the last customer she sold i an orange more than half she now had, leaving her none.

Can you tell the number of oranges she originally had? Oh, by the way, she never had to cut an orange.

10. I'LL GET IT FOR YOU WHOLESALE...

A wholesale merchant came to me one day and posed this problem. Every day in his business he has to weigh amounts from one pound to one hundred and twenty-one pounds, to the nearest pound. To do this, what is the minimum number of weights he needs and how heavy should each weight be?