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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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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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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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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