As a result of temporary magical powers, you have made it to the Wimbledon finals and are playing Roger Federer for all the marbles. However, your powers cannot last the whole match. What score do you want it to be when they disappear, to maximize your chances of hanging on for a win?
It sounds obvious that you should ask to be ahead two sets to love (it takes 3 out of 5 sets to win
the men’s), and in the third set, ahead 5-0 in games and 40-love in the sixth game. (Probably you
want to be serving, but if your serve is like mine, you might prefer Roger to be serving the sixth
game down 0-40 so that you can pray for a double fault.)
Not so fast! These solutions give you essentially 3 chances to get lucky and win, but you can
get six chances—with three services by you and three by Roger. You still want to be up two sets
to none, but let the game score be 6-6 in the third set and 6-0—in your favor, of course—in the
tiebreaker.
Augustus loves candy and much to his delight, his three favorites are on sale. One each of gum, chocolate and caramel cost 40 cents. A caramel is over three times the price of gum. Six gums are worth more than chocolate. A caramel plus two gums cost less than chocolate. What is the price of each candy?
Kevin, Charles, Larry and Alex are in a room that’s about 110 feet long. In front of them are 5 balls which are exactly 100 ft from the exit. The balls are yellow, purple, green, red and blue, respectively. Each man must carry a ball to the exit. After traveling 20 ft a ball will change color twice. The sequence of color changes is always the same: yellow, purple, green, red, and blue.
At 80 ft Kevin’s ball is red.
At 40 ft Larry’s ball is purple.
At 60 ft Charles’ ball is blue
At 100 ft Alex’s ball is purple.
The remaining ball was blue. Here’s a table of each ball and the color it changes to at 20, 40, 60, 80 and 100 ft. Kevin’s started out yellow, Larry’s was green, Charles’ was red and Alex began with a purple ball, leaving blue as the one nobody picked.
You walk into a room and see a bed. On the bed there are two dogs, four cats, a giraffe, five cows and a duck. There are also three chickens flying above the bed. How many legs are on the floor?
Since all of the animals are on the bed and no other furniture is mentioned in the room, there are six legs on the floor. Four legs from the bed and your own two legs as you stand in the room, amazed that someone managed to get so many animals onto a bed. And the ceiling must be vaulted to fit a giraffe. Also, who’s on cleanup duty?
Fence. Fences keep ne’er-do-wells out and protect people inside. A fence is a person who buys stolen goods to later resell them for a profit. Those who fence practice the sport of fencing. En garde! And people don’t like it when you sit on the fence in a heated debate. (Believe me, I speak from experience)
I hesitated to add this because it’s poorly worded, ambiguous and the answer could be almost anything. I prefer teasers with a single answer, but there you go.
If you came up with a different answer and can explain how you did it, don’t think you’re wrong. It’s probably just as valid. Feel free to share yours in the comments.
My answer for the first number is 2.
Here’s how I got it.
The generic rule for a number in the sequence is: 2^(n – 1) + 1, where n is the position in the sequence.
Note: The teaser doesn’t specify the position of 17. In this case, it’s fifth.
Position 1: (so n = 1) is 2^(1 – 1) + 1 = 2
Position 2: 2^(2 – 1) + 1 = 3
Position 3: 2^(3 – 1) + 1 = 5
Position 4: 2^(4 – 1) + 1 = 9
Position 5: 2^(5 – 1) + 1 = 17
For the curious, the next 5 numbers of the sequence would be: