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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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