❔ You have 1,000 bottles of wine. One bottle is poisoned. You have ten rats to test the wine for you. The poison takes effect after one hour. How can you find the poisoned bottle after one hour but not longer than 2 hours?

**Numbering and Binary:**Number the wine bottles from 1 to 1000. Then, convert each bottle number into its binary equivalent. For example:Bottle 1:

**0000000001**Bottle 5:

**0000000101**Bottle 1000:

**1111101000**

**Assignment:**Assign each of the ten rats a digit position in the binary numbers. e.g the 1st rat to the 1st position, the 2nd rat to the 2nd position and so on…**Wine Sampling:**For each bottle of medicine labeled X, all the rats in the positions corresponding to the number 1 in the binary representation of X will be given a sample to drink from that bottle.**Waiting and Observation:**After one hour, observe which rats have died. The binary number formed by their assigned digit positions (1 for dead, 0 for alive) will be the decimal number of the poisoned bottle.

**Example:**

Let’s say bottle number 742 is poisoned. In binary, 742 is **1011100110**.

Rat 1: Drinks (1)

Rat 2: Doesn’t drink (0)

Rat 3: Drinks (1)

Rat 4: Drinks (1)

Rat 5: Drinks (1)

Rat 6: Doesn’t drinks (0)

Rat 7: Doesn’t drinks (0)

Rat 8: Drinks (1)

Rat 9: Drinks (1)

Rat 10: Doesn’t drinks (0)

After an hour, rats **1, 3, 4, 5, 8** and **9** die. This forms the binary number **1011100110**, which converts back to **742** in decimal.