Puzzle | Poison and Rat

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 log_⁡2 1000≈10, we need 10 bits to uniquely represent each bottle from 1 to 1000 in binary.

• Steps 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.