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Seven Puzzles for the Seventh Month

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The Old Bridge

Four people with one flashlight between them have to cross a rickety two-person capacity bridge in the next 17 minutes before a hurricane destroys it: Alice (who takes one minute to cross), Bill (two minutes), Cassie (five minutes) and Dave (10 minutes). It's pitch black, so anyone crossing needs the flashlight. How do they do it?

Gender Gap

In Ruritania, each couple stops having children if, and only if, they have a female baby. After many generations, what will the sex ratio in this country be? (a) Significantly more males than females; (b) Significantly more females than males; (c) Approximately 1:1

Assume: no multiple births; equal probability of a birth being male or female; life expectancy is the same for males and females.

Yin and Yang

Bisect (into equal areas) both the yin and the yang with one straight line.

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Four Cards

Each of four cards has a letter on one side and a number on the other.

Which cards must be turned over in order to check if the statement "Every card with a D on one side has a 3 on the other" is true?

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Harry S Truman

What does the "S" stand for?

Percentages

One hundred percent divided by 10 percent = (a) 0.1 percent; (b) 1 percent; (c) 10 percent; (d) 100 percent; (e) 1,000 percent.

Circles

The sum of the yellow areas is (a) less than; (b) equal to; (c) more than the sum of the blue areas.

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Bonus Question!

What do Ellis Bell, Ann Landers, Robert Galbraith, Anne Rice and George Orwell have in common, literary-wise?

Answers on next page …



Answers

The Old Bridge

Alice and Bill cross (two minutes elapsed); Alice returns with the flashlight (three minutes); Cassie and Dave cross (13 minutes); Bill returns with the flashlight (15 minutes); Alice and Dave cross (17 minutes total).

Gender Gap

(c), since every birth has a 50/50 chance of being male. (Past results have no effect on the probability of the next child's gender.)

Yin and Yang

The small white and black semicircles above and below the horizontal line each have 1/8 of the area of the whole (since the area of a circle is proportional to its diameter squared), as do the two triangles (45 degrees being 1/8 of a full circle). Hence the white area above the 45 degree line has ¼ the area of the whole circle. By symmetry, so does the black area below the 45 degree line. Therefore the 45 degree line bisects both the white and black shapes.

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Four Cards

Cards 1 and 4. Obviously, you have to check card 1 to see if there's a 3 on the back. Card 2 is irrelevant. So is card 3, since whether there's a D or not doesn't affect the validity of the statement. But if there's a D on the back of card 4, the statement is false. (In a test of this logic puzzle, devised by psychologist Peter Wason in 1966, only 10 percent of the general public and 43 percent of mathematicians got it right!)

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Harry S Truman

S

Percentages

(e) (1 divided by 1/10 = 10)

Circles

(b) Each small circle has 1/4 the area of the big circle, so their total area is equal to that of the big circle. Thus, the total area of the overlaps (yellow) must be equal to the total area not covered by the small circles (blue).

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Bonus

All are pseudonyms: Ellis Bell was Emily Bronte, Ann Landers was Ruth Crowley (later, "Eppie" Lederer), Robert Galbraith is J.K. Rowling, Anne Rice is Howard Allen O'Brien, George Orwell was Eric Arthur Blair.

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