You are hosting a big party tonight and prepared 1000 bottles of wine. A spiteful neighbor sneaks in and poisons exactly one bottle. The poison is colorless, tasteless, and takes about an hour to take effect and kill. Your party also starts in an hour, and you don’t want to throw all the wine away.

You have 10 mice and time for only one round of tasting. In that round, a mouse can taste from any number of bottles. How can you identify that single poisoned bottle among 1000?

Pause here and try to solve the problem yourself!

An obvious solution might be to group the wine into 10 batches of 100 bottles and have each mouse drink from one batch. But if a mouse dies, you have only narrowed it down to 100 bottles, and there is no time for a second round. Whatever test you run, you only get one shot.

A 300-Year-Old Idea

Some background information before we solve the problem.

In 1703, Gottfried Leibniz published a paper describing how every number can be written using only two symbols: 0 and 1. To him, the concept felt almost divine – an entire universe created out of nothingness and unity. But for over two centuries, binary remained an idea trapped on paper.

Everything changed when a young engineer named Claude Shannon realized that 0 and 1 map perfectly onto the physical states of an electrical switch: off and on. That single insight laid the groundwork for digital circuits, eventually powering every smartphone, laptop, and text message on the planet.

Yet binary is more than just how machines store information. It is a way of extracting information.

0 and 1 not only reflect the underlying logic of switches, but they also correspond to every yes/no question you ask: “did this mouse die, or not?”. And 10 binary digits can cover 2¹⁰ = 1024 different possibilities.

The Solution  

Step 1: Relabel the bottles in binary

Write each bottle’s number, 1 through 1000, as a 10-digit binary number, padding the front with 0s. For example, bottle 17 is 10001 in binary, so its label becomes 0000010001. Every bottle now carries a unique 10-digit barcode of 0s and 1s.

Step 2: Assign each mouse a digit

Line up the mice and assign each one a digit: mouse #1 owns the leftmost digit, mouse #10 the rightmost. Then, run the tasting by the simple rule of a mouse drinks from a bottle if and only if its digit in that bottle’s label is a 1.

For bottle 17, only mouse #6 and mouse #10 take a sip. No two bottles are sampled by the same combination of mice; each bottle’s binary label is its unique drinking pattern.

Step 3: Read the answer off the casualties

One More Sip

Before you pop the corks, one last question: was the binary system essential here, or could we have used a different method?

Here’s a food for thought: suppose your neighbor used a cheaper poison that kicks in 30 minutes instead of an hour, now there is time for a second round of tasting.

Now each mouse has three possible outcomes instead of two: dies in round 1, dies in round 2, or survives. Binary is the wrong language here; you want base 3.

The scheme goes as follows. Label the bottles in base 3, give each mouse a digit position, and follow one rule: if digit 1, drink in round 1; if digit 2, drink in round 2; if digit 0, sit out. Each mouse’s fate is its digit on the poisoned bottle’s label.

That is the lesson hidden in the wine cellar. The binary system is more than the foundation of our telecom network, it is also a way of thinking – a reminder that any question, no matter how large, can be answered by a patient sequence of yes and no. You walked into an impossible evening with ten mice and walked out with 999 bottles of perfectly good wine.

Enjoy the party.