Quantitative Analyst Interview Questions

Chapter 7.2, P.183 in Zhou's book

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.

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

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.

The answer is 1023. 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.

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.