How can you tell which bottle of wine is posioned when have thirteen bottles four lab rats and only one posioned?

The Strategy

The key is to use binary numbers to represent each bottle.

1. Number the Bottles: Assign each bottle a number from 1 to 13.

2. Binary Representation: Convert each bottle number into its binary equivalent. Since the highest number is 13 (which is 1101 in binary), you'll need four digits to represent all bottles.

3. Feed the Rats: Each rat will represent a specific digit in the binary number. For example:

* Rat 1: Represents the rightmost digit (the "1's place").

* Rat 2: Represents the second digit from the right (the "2's place").

* Rat 3: Represents the third digit from the right (the "4's place").

* Rat 4: Represents the leftmost digit (the "8's place").

4. Give Wine: Give each rat wine from bottles whose binary representation has a "1" in the digit that rat represents.

5. Observe the Rats: After a certain time, observe which rats die. The binary number formed by the dead rats (where "1" represents a dead rat and "0" represents a live rat) will be the number of the poisoned bottle.

Example:

Let's say bottle number 5 is poisoned.

* Bottle 5 in binary is 0101.

* Rat 1: Gets wine from bottles 1, 3, 5, 7, 9, 11, 13 (all odd-numbered bottles)

* Rat 2: Gets wine from bottles 2, 3, 6, 7, 10, 11 (all bottles with a "1" in the 2's place)

* Rat 3: Gets wine from bottles 4, 5, 6, 7 (all bottles with a "1" in the 4's place)

* Rat 4: Gets wine from bottles 8, 9, 10, 11, 12, 13 (all bottles with a "1" in the 8's place)

If Rat 1 and Rat 3 die, the binary number formed is 0101, which is the decimal representation of 5. Therefore, bottle 5 is poisoned.

Let me know if you'd like to work through a specific scenario to see this in action!