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Miscellaneous Puzzles on Mental Calculation Set 3

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When Longfellow was Professor of Modern Languages at Harvard College he was accustomed to amuse himself by giving more or less simple arithmetical puzzles to the students. Here is an example: If one-fifth of a hive of bees flew to the ladamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbor, and one bee continued to fly about, attracted on each side by the fragrant ketaki and the malati, what was the number of bees?

Correct! Wrong!

The number of bees must have been 15.

Me and Bill," said Casey, "can do the job for you in ten days, but give me Alec instead of Bill, and we can get it done in nine days."

Correct! Wrong!

Alec could do the work in 1433/49 days; Bill in 17 23/41 days; and Casey in 23 7/31 days

A correspondent (c. H. P.) puts the following little question: An Australian farmer dies and leaves his sheep to his three sons. Alfred is to get 20 per cent more than John, and 25 per cent more than Charles. John's share is 3,600 sheep. How many sheep does Charles get? Perhaps readers may like to give this a few moments' consideration.

Correct! Wrong!

The share of Charles is 3,456 sheep. Probably some readers will first have found Alfred's share, and then subtracted 25 per cent, but this will, of course, be wrong.

A travelling menagerie contained two freaks of nature-a four-footed bird and a six-legged calf. An attendant was asked how many birds and beasts there were in the show, and he said: "Well, there are 36 heads and 100 feet altogether. You can work it out for yourself." How many were there?

Correct! Wrong!

As the menagerie contained two monstrosities-the four-footed bird and the six-legged calf-there must have been 24 birds and 12 beasts in all.

The driver of the taxicab was wanting in civility, so Mr. Wilkins askecl him for his number. "You want my number, do you?" said the driver. "Well, work it out for yourself. If you divide my number by 2, 3, 4, 5, or 6 you will find there is always lover; but if you divide it by II there ain't no remainder. What's more, there is no other driver with a lower number who can say the same." What was the fellow's number?

Correct! Wrong!

The driver's number must have been 121.

A printer had an order for 10,000 bill forms per month, but each month the name of the particular month had to be altered: that is, he printed 10,000 "JANUARY," 10,000 "FEBRUARY," 10,000 "MARCH," etc.; but as the particular types with which these words were to be printed had to be specially obtained and were expensive, he only purchased just enough movable types to enable him, by interchanging them, to print in turn the whole of the months of the year. How many separate types did he purchase? Of course, the words were printed throughout in capital letters, as shown.

Correct! Wrong!

The printer must have purchased the following twenty-seven types:

A salesman packs his dog biscuits (all of one quality) in boxes containing 16, 17, 23, 24, 39, and 40 Ibs. respectively, and he will not sell them in any other way, or break into a box. A customer asked to be supplied with 100 Ibs. of the biscuits. Could you have carried out the order? If not, how near could you have got to making up the 100 Ibs.? Of course, he has an ample supply of boxes of each size.

Correct! Wrong!

The salesman supplied four boxes of 17 Ibs. each, and two boxes of 16 Ibs. each, which would make exactly the 100 Ibs. required

Alfred and Bill together can do a piece of work in twenty-four days. If Alfred can do only two-thirds as much as Bill, how long will it take each of them to do the work alone?

Correct! Wrong!

Here is an example of the elegant way in which Bhaskara, in his great work, Lilivati, in 1150, dressed his little puzzles: The square root of half the number of bees in a swarm has flown out upon a jessamine bush; eight-ninths of the whole swarm has remained behind; one female bee flies about a male that is buzzing within the lotus flower into which he was allured in the night by its sweet odor, but is now imprisoned in it. Tell me the number of bees.

Correct! Wrong!

There were seventy-two bees.

Some sheep stealers made a raid and carried off one-third of the flock of sheep and one-third of a sheep. Another party stole one-fourth of what remained and one-fourth of a sheep. Then a third party of raiders carried off one-fifth of the remainder and three-fifths of a sheep, leaving 409 behind. What was the number of sheep in the flock?

Correct! Wrong!

The number of sheep in the flock must have been 1,025. It will be found that no mutilation of any sheep was necessary.

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