You have 1000 wine bottles. Exactly one bottle is poisoned.
- A rat that drinks the poisoned wine will die within 1 hour.
- Assume rats can each sip any number of samples once at the start.
Determine the minimum number of rats needed to identify which single bottle is poisoned in 1 hour.
Check if you were right - full answer with solution below.
Solution:
To identify the poisoned bottle among 1000 within an hour, we use 10 rats and the binary number system. Since logā”2 1000ā10, we need 10 bits to uniquely represent each bottle from 1 to 1000 in binary.
- Step 1: Number the bottles from 1 to 1000 and convert each number to its 10-bit binary equivalent.
- Step 2: Assign each rat to a specific bit position (Rat 1 - bit 1, Rat 2 - bit 2, ..., Rat 10 - bit 10).
- Step 3: If a bottle has a 1 in a certain bit position, the corresponding rat drinks from it.
- Step 4: After one hour, the combination of rats that die reveals the binary number of the poisoned bottle.
Example: If Rats 5, 7, and 9 die, the binary pattern is 0000101010, which equals 42 in decimal. So, Bottle 42 is the poisoned one.
