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If You Score 4/6 On This Brain Teasers Math Quiz, You Are Really Smart

This quiz may melt your brain. Hope you liked having an unmelted brain.

These brain teasers were provided by the National Museum of Mathematics in New York City. It has fun exhibits for people of all ages and all math abilities.

  1. How many people is "two pairs of twins twice"?



    If you thought the answer was 16, you are not alone. But a twin is only one person; a pair of twins, just two. Two pairs of twins equal four. Twice that is eight.

  2. The three volumes of Lord of the Rings sit in order on a shelf. Each is 1 1/4 inches thick, comprising an inch of pages and 1/8 inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?


    1 1/2 inches.

    Seems like it should be 3 1/2 inches, doesn't it? But if you think about where page 1 of volume I is when the books are lined up the usual way (volume I on the left), you'll see that the worm actually passes through only one volume's worth of pages.

  3. A pencil with a pentagonal cross section has the maker's logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?



    The pencil will always land with a face of the pentagon down โ€” and thus with an edge, not a face, pointing straight up.

  4. A visitor points to a portrait on the wall and asks who it is. "Brothers and sisters have I none," says the host, "but that man's father is my father's son." Who is pictured?


    The host's son.

    The phrase "my father's son" can only refer to the host himself, since he has no brother. So the quotation is equivalent to "That man's father is me."

  5. How many Friday the 13ths can there be in one calendar year?



    This is an exercise in counting modulo 7. But even if you don't know what that means, you can solve the puzzle by first assuming that Jan. 13 is a particular day of the week (say, Sunday, as it was for 2019). Then Feb. 13, March 13, etc., would be Wednesday, Wednesday, Saturday, Monday, Thursday, Saturday, Tuesday, Friday, Sunday, Wednesday, Friday. Since the most one day appears on this list is three times (Wednesday), we could shift so that there are three Friday the 13ths. Note that all days of the week do appear at least once, so every year has at least one Friday the 13th. It remains to check leap years to make sure that you can't get more than three Friday the 13ths, and in fact, leap years can only get two (but again, always at least one). (By the way, it's a curious artifact of our Gregorian calendar that in a calendar cycle, which is 400 years long, the 13th of the month falls more often on a Friday than on any other day of the week.)

  6. One carafe contains a liter of wine, another a liter of water. A spoonful of wine is moved from the wine carafe to the water carafe and mixed in. A spoonful of the mixture is then moved from the water carafe to the wine carafe.


    Same in both.

    It seems like, since you transferred pure wine to the water and only a mixture back, there must be more wine in the water than water in the wine. But that can't be right because then you would have increased the total amount of wine! No matter what you do, if you end with a liter of liquid in each carafe, there must be the same amount of wine in the water carafe as there is water in the wine carafe. The flaw in the first argument is that although you transferred less than a spoonful of water to the wine carafe, you returned some of the wine.

Don't forget: Check out the National Museum of Mathematics in New York City. It's great for people of all ages and all math abilities. You can also find cool gifts for everyone in the family. It doesn't matter how many of these you got right โ€” check it out if you're in New York City!

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