**Amazon Interview Question** Half the cable length is 40 feet, so the cable must be hanging straight down, i.e. the poles are touching.

**Live Another Day** The outcome of the two tosses will either be the same or different, so they decided on a simple strategy: Tulip will always predict the same (e.g. she sees a head and predicts Jesse will see a head) while Jesse will always say the opposite (e.g. he sees a head and guesses Tulip saw a tail). One of their guesses will always be correct.

**Go for the Girls!** It's 50/50, since each baby born is as equally likely to be a boy as a girl, no matter what the king says.

**More Girls** 1 in 3. She might have (in birth order) girl-girl, girl-boy or boy-girl. Only one of these three options results in her other child being a girl.

**Triangles** There are 18 triangles.

**Timepieces** Sundial; hourglass.

**Race** Second.

**Letters** ITS (In The Sequence).

**Dormitory** Dirty room.

**Roman Numerals** Turn it upside down.

**1876 MIT Entrance Exam** They are 50 and 18. (Two years ago, they were 48 and 16; in 14 years, they will be 64 and 32.)

**Sum** S = 1 + 1/2 + 1/4 + 1/8 ...; S/2 = 1/2 + 1/4 + 1/8 ...; subtract, canceling out everything except the 1, giving you S – S/2 = 1, QED.

**What's the Area?**It's 28 cm2. Draw lines from each corner to the point inside the square, forming eight triangles. Since each pair of triangles on a side have the same area (equal base and height), the blue area (a + d) = (a + b) + (c + d) – (b + c) = 16 + 32 – 20 = 28.

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