Goldman Sachs Interview Question: You have 10 mice and 1000 bot... | Glassdoor

## Interview Question

Quantitative Analyst Interview London, England (UK)

# 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.

2

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.

Robert on May 19, 2013
26

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.

Peter on May 22, 2013
0

Matt on Sep 30, 2013
0

Chapter 7.2, P.183 in Zhou's book

Tony on Oct 14, 2013
12

Encode the wine bottle numbers in binary. Give each mouse is a combination based on this table:

| mouse | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|-----------|---|---|---|---|---|---|---|---|---|---|---|
| wine 1 | - | - | - | - | - | - | - | - | - | - | - | - |
| wine 2 | - | - | - | - | - | - | - | - | - | - | - | + |
| wine 3 | - | - | - | - | - | - | - | - | - | - | + | - |
| wine 4 | - | - | - | - | - | - | - | - | - | - | + | + |
...
| wine 1000 | + | + | + | + | + | - | + | - | - | - |

If none of the mice die, wine bottle 1 contains the poison.
If only mouse 10 dies, wine bottle 2 contains the poison.
...
If mice 1-5 and 8 die, wine bottle 1000 contains the poison.

That systems allows for an additionally 24 bottles to be encoding, 2^10=1024.

Brian Spiering on Apr 2, 2015
0

10 mices vs 1000 bottles
1 mice per 100 bottles
24 hiurs one dies 9 alive
100*9=900

gintaras on Dec 20, 2016
0

The answer is 900. You have 1000 bottles divided between 10 mice. as dosage doesn't matter, 100 bottles can contribute to a single dosage, in which case, one mouse will die meaning the tainted batch needs to be discarded and 900 are confirmed untainted.

Anonymous on Dec 20, 2016
0

You need to think in bit-wise way. 1023 can be represented in binary as (1111111111). Your goal should be: representing each wine label (i-th number) to each binary representation. 1000th wine will be represented with 1111101000 meaning (1,2,3,4,5,7th) mices will be used to check the toxicity of this wine.
In binary way, you can assign label to up to 1023 wines.
So by analysing the rats that die after 24 hrs, you can actually identify which wine is toxic or not. hope this helps.

jw on Aug 29, 2017
0

Brian was quite close, but to represent 1024 wines, you actually need 11 mice. So the maximum # of wines that one can guarantee is up to 1023.

jw on Aug 29, 2017