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You have 10 mice and 1000 bottles of wine. You also have 24 hours before a party, and one of the bottles has been tainted with a slow acting poison, which takes 24 hours to kill a mouse. In the 24 hours you have remaining, how many bottles can you guarantee safe for human consumption (assume humans and mice react identically)? Assume the lethal dosage is insignificant relative to the size of the bottle.

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I'll say 500. Since the dosage is insignificant, I'll divide the number of bottles in half, take samples from each of the first 500 bottles, mix them up, divide by 10 and feed to each mouse. If no mouse dies after 24 hours, then the first batch is safe. else, the second batch would be served.

999. It is like a binary problem. First mouse tests the first #1-500 (mixed). Second tests #1-250 and #501-750. Third one tests #1-125, #251-375, #501-625, #751-875, and so on. 10 mice with 2 status each (death/alive) could encode number of bottles up to 2^10=1024. So 10 mice is enough to find out the single bottle that tainted.

http://advanceddiscrete.wikispaces.com/Mice+and+Wine

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a, b, c are integers. Such that a^2 + 2bc = 1; b^2 + 2ac=2012, find all the possibles values of c^2 + 2ab.

7 Answers

You have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a pair of cards are both red, then you win that pair; if a pair of cards are both black, then I win that pair; if a pair of cards has one red and one black, then it's discarded. If, after going through the whole deck, you have more pairs than I do, then you win $1, and if I have more pairs than you do, I win $1. What is the value of this game in the long run?

9 Answers

A = Sqrt(E(Variance)) B = E(Sqrt(Variance)) Is A larger or B larger? Please explain.

5 Answers

Round 2: If you have balls weighting from 1, 2, ... 40g, and you have a fair balance, how many of their weights you have to know in advance such that you can measure all the rest?

5 Answers

derive the formula for the variance of OLS from scratch

4 Answers

What is the price of a contract that at time T=2 pays out S_2 / S_1. Interest rate is continuous and equal to r?

3 Answers

First round: basic probability, combinatorics. A bear wants to catch 3 fish from a river. when he has caught 3 fish, he'll leave. when a fish comes, there is a 1/2 chance he'll catch it. what's the probability that the 5th fish will not be caught?

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If a car takes one lap with 20 k/h, how fast should it go the second lap to get the average of the first and second laps equal to 25 k/h?

3 Answers

What kind of subjects are you looking to teach?

3 Answers
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