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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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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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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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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