In the Clock Game, part of the game show The Price Is Right, a contestant must
guess the price (rounded to the nearest dollar) of a prize which is worth less than $2,000. After
each guess, the contestant is told whether her guess was correct, too low, or too high. Assume
that the contestant is mathematically savvy but has no idea how much the prize is worth.
With how many guesses is she guaranteed to win the prize? Choose the correct choice from the following answers:	A) 10	B) 11	C) 12	D) 13	E) 1997
At each stage, the contestant has narrowed the range of possible prices to an interval,   and she should guess exactly in the middle this interval. For example, for the first guess she   should guess either $1,000 or $1,001. (On the actual show, your time is limited rather than   the number of guesses, so you should start with $1,000 because it is quicker to say.)   At every step the contestant can at least halve the number of remaining possibilities.   Suppose that the interval has n possible prices and that the contestant's guess does not win   immediately. If n is odd there will be n􀀀1   2 prices on either side of her guess, and she will be   told which of these contains the correct price. If n is even then there will be n   2 prices on one   side n   2 *1 prices on the other, and we assume the worst case of n   2 .   Since 210 = 1024 and 2000   1024 &lt; 2, after ten guesses she will be down to one remaining   possibility, which she guesses with her eleventh guess.   Conversely, ten guesses is not enough. After each the remaining number of possibilities   could be as high as: 1000,500,250,125,62,31,15,7,3. She is guaranteed only a 1-in-3 shot in   the tenth guess.   correct answer 11
<result>B</result>
In the Clock Game, part of the game show The Price Is Right, a contestant must
guess the price (rounded to the nearest dollar) of a prize which is worth less than $2,000. After
each guess, the contestant is told whether her guess was correct, too low, or too high. Assume
that the contestant is mathematically savvy but has no idea how much the prize is worth.
With how many guesses is she guaranteed to win the prize?