Puzzles
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7. Guess the right number correctly.
Ask anybody to jot down any three-digit number, and then to repeat the digits in the same order to make a six-digit number (e.g. 345345, 456456). With your back turned so that you cannot see the number, ask him/her to pass the sheet of paper to another body, who is requested to divide the number by 7.
'Don't worry about the remainder,' You tell him, 'Because there won't be any.' He/She is surprised that you are correct. (e.g. 345345 divided by 7 is 49335). Without telling you the result, he/she passes this number to the another guy, who is told to divide it by 11. Once again there is no remainder, you insist. And again you are correct. (e.g. 49335 divided by 11 is 4485).
With your back still turned, and no knowledge whatever of the figures obtained by these computations, you pass this number to the last guy, and ask him/her to divide the number by 13. Again there is no remainder. (e.g. 4485 divided by 13 is 345). This final result is written on a slip of paper which is folded and handed to you. And you open it. And you said, 'It is the original three-digit number the first person jot down'.
Show that this trick cannot fail to work regardless of the digits chosen by the first person.
(Click the link at the bottom of this page for solution)
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8. Hole in the sphere.
This problem requires calculations and it seems to lack sufficient data for a solution. A cylindrical hole six inches long has been drilled straight through the centre of a solid sphere. What is the volume remaining in the sphere?
(Click the link at the bottom of this page for solution)
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9. The matches.
Assuming that a match is a unit of length, it is possible to place 12 matches on a plane in various ways to form polygons with integral areas. The illustration shows two such polygons: a square with an area of nine square units, and a cross with an area of five. Like the pictures below.
The problem is this: Use all 12 matches (the entire length of each match must be used) to form in similar fashion the perimeter of a polygon with an area of exactly four square units.
(Click the link at the bottom of this page for solution)
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10. Water and wine
There are two beakers. One containing water, the other wine. A certain amount of water is transferred to the wine, then the same amount of the mixture is transferred back to the water. Is there now more water in the wine than there is win in the water? Simple calculations show that the two quantities are the same.
Now there is a further question: Assume that at the outset the beaker holds 10 ounces of water and the other holds 10 ounces of wine. By transferring three ounces back and forth any number of times, stirring after each transfer, is it possible to reach a point at which the percentage of wine in each mixture is the same?
(Click the link at the bottom of this page for solution)
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11. An absent-minded teller
A bank teller switched the dollars and cents when he cashed a check for Mr. Brown, giving him dollars instead of cents, and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had left exactly twice as much as his original check.
What was the amount of the check?
(Click the link at the bottom of this page for solution)
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12. White, black and brown
Merle White, Jean Brown and Leslie Black are lunching together.
'Isn't it remarkable,' observed the lady, ' that our last names are Black, Brown and White and that one of us has black hair, one brown hair and one white. '
'It is indeed' replies the person with black hair, ' and have you noticed that not one of us has hair that matches his or her name?'
'Opps, you are right' exclaimed Mr. White.
If the lady's hair isn't brown, what is the color of Mr. Black's hair ? (Hint: Who is the lady? You have to answer this question first )
(Click the link at the bottom of this page for solution)
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