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Showing posts with label Quiz. Show all posts
Showing posts with label Quiz. Show all posts

Sunday, August 31, 2008

Sentence to Freedom

A peasant is convicted in China. He gets the death penalty. The judge allows him to say a last sentence in order to determine the way the penalty will be carried out. If the peasant lies, he will be hanged. If he speaks the truth he will be beheaded. The peasant speaks a last sentence and everybody surprise some minutes later he is get free because the judge cannot determine his penalty. What did the peasant said?


SOLUTION :

The peasant said:"I shall be hanged!". -QED-

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Thursday, July 31, 2008

It's always

It's always 1 to 6
it's always 15 to 20
it's always 5
but it's never 21
and if 21, it's flying.




SOLUTION :
a dice.
It's always 1 to 6 : the numbers on the faces of the dice,
it's always 15 to 20 : the sum of the exposed faces when the dice comes to rest after being thrown,
it's always 5 : the number of exposed faces when the dice is at rest,
and if 21 it's flying : the run of all exposed faces when the dice is flying.

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Monday, June 30, 2008

Math's Sentences

In this sentences. There is ... The numbers of 0. And ... The numbers of 1. And ... The numbers of 2. And ... The numbers of 3. And ... The numbers of 4. And ... The numbers of 5. And ... The numbers of 6. And ... The numbers of 7. And ... The numbers of 8. And ... The numbers of 9.



SOLUTION :

Respectively 1 7 3 2 1 1 1 2 1 1. -QED-

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Saturday, May 31, 2008

Trains

A train leaves Los Angels for New York every hour on the hour. A train leaves New York for Los Angels every hour on the half hour. The trip takes five hours each way.
As you ride from Los Angels to New York, how many of the trains bound from New York to Los Angels would you pass?



SOLUTiON :

You would pass the first train returning to Los Angels fifteen minutes after you start(you are fifteen minutes out of Los Angels and the other train is due in Los Angels fifteen minutes later) and one each half hour there after.
You will pass ten trains bound for Los angels. -QED-

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Wednesday, April 30, 2008

Time

Simpkins and Green made arrangements to meet at the railroad station to catch the eight o'clock train to Philadelphia. Simpkins thinks that his watch is twenty five minutes fast although it is in fact ten minutes slow. Green thinks his watch is ten minutes slow, while it actually has gained five minutes.
What will happen if both men, relying upon their watches, try to arrive at the station five minutes before train time.



SOLUTION :

Simpkins thinks he will be in plenty of time when his watch shows 8:20, but it is already 8:30, much too late to catch the train. But Green will reach the station when his watch shows 7:45, and since his watch is five minutes fast, he will really be there at 7:40, twenty minutes ahead of train time. -QED-

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Saturday, March 29, 2008

Window Washing

When Mr.Watson built his home, he made one wall of the living room entirely out of thick plate glass. He soon realized how expensive as well as inconvenient it was to live in a "glass fishbowl", for the glass had to be washed on the average of once a week. It was too big a job for him, since the wall measured nineteen by twenty feet, so he contracted with a window cleaning service to do the full job once a week at the cost of one dollar per hundred square feet of surface washed, what was Watson weekly bill?



SOLUTION :

The "full job" would have to include both the inside and outside 2 times 19 times 20 equals 760 square feet of surface to be washed. The bill was thus $7.6 per week. -QED-

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Friday, February 29, 2008

The Empty Flask

An apothecary found six flasks capable of holding sixteen, eighteen, twenty-two, twenty-three, twenty-four, and thirty-four fluid ounces respectively. He filled some with distilled water and then filled all but one of the rest with alcohol, nothing that he had used twice as much alcohol as water.
Which flask was left over? And which flasks were used for distilled water, which for alcohol?



SOLUTION :

Since the apothecary had used twice as much alcohol as water, the total ounces of alcohol and water together must be divisible by 3. The total capacity of all 6 flasks is 137 ounces, a number which is 2 more than a multiple of 3. Because the apothecary left one flask empty, it is obvious that this flask must have had a capacity in ounces which is 2 more than a multiple of 3. The only flask which meets this requirement is the one with a capacity of 23 ounces. This flask must have been the one left empty. The remainder, which have a combined capacity of 114 ounces, were filled. One-third of this total, 38 ounces, was water. The 16 and 22-ounces flasks must therefore have been used for water and the 18, 24, and 34-ounce flasks used for alcohol. -QED-

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Friday, January 11, 2008

Rare Flowers

It was a day of special joy for Mrs. Greenhouse. She was exhibiting her collection of rare flowering plants to members of her garden club.
"Now these are my real treasures," she said in her best lecture voice, pointing to three luxuriously flowering specimens. "I got them from Guatemala only a year ago, and I have been giving them my closest attention. They are all quite delicate indeed. Since the flowers last only a single day. The plant with crimson flowers blossoms every fourth day, but I have to wait until the seventh day for the plant with lavender flowers. But that one is the most precious of all," she said, directing attention to her third plant."It takes a full thirteen days for it to blossom."
Since her three tropical flowering plants were such an enormous attraction, Mrs. Greenhouse expansively invited the club members to return to see them again."Let's make it next year on this very same day," she announced, "since they will all be in blossom them."
Was Mrs. Greenhouse correct in her horticultural reckoning?



SOLUTION :

If the club members come a year later on the very same day of the month, they would be one day later for the triple blooming. On the other hand, if they come next year on the very same day of the week(and as nearly as possible a year later), they would be right on time.
The least common multiple of 4, 7, and 13 is the smallest number divisible by all three numbers. Since this number is 4x7x13=364, it can be seen that the three plants blossom simultaneously every 364 days-52 weeks, but one day less than a full year. -Q.E.D-

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Wednesday, December 26, 2007

Chickens

If a hundred chickens eat a hundred bushels of grain in a hundred days, how many bushels will ten chickens eat in ten days?
And if, on the average, one and a half of these chickens lay an egg and a half in a day and a half, how many days will it take a chicken to lay one and a half dozen eggs.



SOLUTION :

The tendency in the first problem is to conclude that if 100 chickens eat 100 bushels in 100 days, one chicken will eat one bushel in one day and any farmer will certainly quarrel with the likelihood of this calculation. The correct reasoning leads to this conclusion: if any number of chickens eat 100 bushels in 100 days, then the same number of chickens will eat one bushel in one day. This reasoning yields the correct answer 10 chickens will eat one bushel in 10 days.
The same process of reasoning leads to 27 days as the time required for one chicken to lay 1 1/2 dozen eggs.

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Ten Digits

1. Arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 in succession using each one only once and, with the aid of plus and minus signs as desired, produce a sum of 100.
2. Add zero to the nine digits above and rearrange them in fraction form to produce a sum of 1.


SOLUTION :

1. 123-45-67+89=100
2. 35/70 + 148/296 = 1/2 + 1/2 = 1
The first answer appears to be unique, but there are numerous ways to rearrange the second answer.-QED-

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Monday, November 19, 2007

The ladder

At a factory fire a fireman stood on the middle rung of a ladder, directing water into the burning building. As the smoke diminished, he stepped up three rung and continued his work from that position. A sudden flare-up of flames forced him to descend five rung. A few minutes later he climbed up seven rungs and worked there until the fire was out. Then he climbed the seven remaining rungs and entered the factory. How many rungs were in the ladder?

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Monday, November 12, 2007

Average speed

Mr. Sandys took a great deal of satisfaction from the fact that his summer cottage was comparatively close to his office in the city. One friday afternoon he got an early start and was able to make trip to the cottage at an average speed of sixty miles an hour. But he overslept on Monday morning and by the time he got on his way to the city the traffic was so heavy that he averaged only thirty miles an hour. By the time he reached his office, Mr. Sandys was weary and much less satisfied with the convenience of his week-end retreat.
What was his average speed for the round trip?


Solution :
Forty miles an hour. This figure holds true on matter what the distance may be. For example, assume that the trip from city to summer cottage covered 120 miles. On the trip out to the country Mr. Sandys averaged 60 miles an hour, thus taking two hour to cover the distance. Since he made the trip back to the city at an average speed of 30 miles an hour, he took four hours over the same distance. In all, the round trip of 240 miles took him six hours, thus giving him the 40 mph average. -QED-

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Seven loaves of bread

Three travelers meet. They sit down to eat. One traveler produces three loaves of bread, the second traveler produces four loaves. After the seven loaves are divided equally and eaten, the third traveler produces seven dimes and says, "Please divide there dimes equitably between the two of you."How much money should each of the first two travelers receive?



Solution :
The key is the word equitably. At first glance it may appear that the first traveler should receive three dimes and the second should get the remaining four, but this would not be equitable. Each traveler has eaten 7/3 loaves of bread. The first traveler and the second traveler contributed (3-7/3)=2/3 loaves to the third traveler and the second traveler contributed (4-7/3)=5/3 loaves to the third traveler. For the distribution to be equitable, the first traveler should receive two dimes and the second traveler five dimes. -QED-

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Mother's little kitchen helper

If it take 3 3/4 minutes to boil one egg, how long does it take to boil six eggs?



Solution :>
3 3/4 minutes, provide you boil them all at the same time. -QED-

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Sunday, November 11, 2007

The erudite bookworm

The bookworm is a staple character in puzzle literature. Ours, finding himself in a library in which the sets of books were placed in the usual sequence, decided to sample some Shakespeare from a two-volume edition on a bottom shelf. Begining with the foreword of volume 1 and boring through in a straight line to the last page of volume 2, the bookworm made his way at the rate of one inch every four days. He each cover is an eighth of an inch thick, and if each volume measure three inches in thickness, how long will it take the erudite bookworm to digest his way through Shakespeare?



Solution :
Since this library is arranged in usual order, Volume 1 will be to the left of Volume 2, The Foreword of Volume 1 and the last page of Volume 2 will be separated only by two covers a distance of 1/4 inch. At his specified rate of travel, the bookworm will munch his way through this distance in one day. -QED-

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Saturday, November 10, 2007

The bright graduate

Young Smitherly, who was about to graduate at the head of his class at Upcoming University, was in the pleasant position of having his choice of two very attractive offers both at $5000 a year. Unable to make up his mind between them immediately, he wrote the two companies and asked what his chances were for raises over the next five years.
Company A replied to the effect that it would guarantee a raise of $300 every six month for the next five years. Company B said it would guarantee a raise of $1200 every twelve months for the next five years.
To the astonishment of his father, Smitherly accepted Company A's offer. Why?



Solution :
During each year Smitherly would receive the following from the two companies :
Year first
A>2500+2800=5300
B>5000
Year second
A>3100+3400=6500
B>6200
Year third
A>3700+4000=7700
B>7400
Year fourth
A>4300+4600=8900
B>8600
Year fifth
A>4900+5200=10100
B>9800
in the other words, Company A's offer is $300 a year better than Company B's.
This looks like paradox but it isn't. A raise in semiannual pay of $300 is the same as a raise of $600 in annual pay. Since Company A was offering two such raises, or $1200 a year, it was equivalent to Company A's offer except that, as a result of the semiannual feature, each year he would get $300 of this $1200 raise six months earlier. -QED-

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Friday, November 09, 2007

Bargain day

On the final day of his close-out sale, a merchant hastily disposed of two lamps at the bargain price of twelve dollars apiece. He estimated that he must have made some profit on the combined transactions since he made a 25 per cent profit on one and only took a 20 per cent loss on the other. Was he correct in his quick estimate?



Solution :
No.
$12.00 is 125% of $9.60--$2.40 profit
$12.00 is 80% of $15.00--$3.00 loss
He will $0.60 net loss. -QED-

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The enterprising snail

A group of snails had been living happily for many years at the bottom of a twenty foot well when it suddenly ran dry. Most of the snails lay down to did, but one industrious fellow decided to in elsewhere. The next dawn he began to climb to the top of the well at the prodigious rate of three inches per hour for each of the twelve daylight hours. Each night, however, he slipped back at the rate of two inches per hour. How long did it take this enterprising snail to escape from the well?



Solution :
17 1/2 days. The snail climbed at the net rate of one foot per day (3-2=1). At dawn of the start of the eighteenth day he was, therefore, 17 feet from the bottom or 3 feet or 3 feet from the top. Since he climbed 3 feet during the twelve daylight hours of the eighteenth day he would reach the top at sunset of the eighteenth day, or 17 1/2 days after he started his climb. -QED-

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