Imagine this. It’s the eve of the annual Bankers State Association Banquet. The treasurer has procured the food and the wine for the following evening’s gala, and he’s extremely pleased with himself because he knows a guy, who knows a guy, who knows a guy, and for only $50 he’s obtained fourteen one-half gallon jugs of the finest red wine. He’s very excited about the following evening’s festivities until he receives an anonymous note suggesting that one of those bottles of wine may be poisoned!
Because they’re hopeless cheapskates and unwilling to discard 14 bottles of perfectly good cheap wine, the bankers consult with a scientist friend of theirs. “So let’s see,” he says, “you have these sixteen bottles of wine and one of them may be poisoned.”
The scientist goes on to suggest that from his knowledge of poisons, even the smallest sample is usually enough to cause certain death, even if mixed and diluted with the wine from the untainted bottles. “Hmmmmm,”’ he says. “I’ll be right back.”
In a flash, he returns with four small cages, each one containing your standard lab rat. “Here you go,” he says.
“But wait, wait,” they say. “We have 14 bottles of wine. How are we supposed to save all the bankers coming to the luncheon tomorrow, with just 4 rats?’”
“You can do it,” he says and then disappears into the inky shadows.
So, you have 4 rats in little cages, 14 bottles of wine and one of them may have poison in it. Now you can obviously take samples from any of the bottles and you can give as much or as little as you want to any of the rats.
The answer: You use unique combinations. With four different variables (i.e. rats) you can create 16 distinct combinations.
Here’s how you do it. Bottle number one goes only to rat one. Bottle number two goes only to rat number two. Bottle number three goes only to rat number three. And bottle number four goes only to rat number four.
Here’s the interesting part. Bottle number five goes to rats one and two. So if rats one AND two are belly up the next day, it can only be because bottle number five had the poison in it. Bottle number six goes to rates one and three. So if rats one AND three are belly up the next day, it can only be because bottle number six had the poison in it.
| Rat | Drinks from Bottle #… |
| 1 | 1, 5, 6, 7, 11, 12, 13 |
| 2 | 2, 5, 8, 9, 11, 12, 14 |
| 3 | 3, 6, 8, 10, 11, 13, 14 |
| 4 | 4, 7, 9, 10, 12, 13, 14 |
Each unique combination corresponds to a different bottle of wine. Here are tables showing what wine to give to each rat, and then how to determine which bottle is poisoned depending on which rats go to rat heaven:
| Rats that perish | Poison Bottle |
| 1 only | 1 |
| 2 only | 2 |
| 3 only | 3 |
| 4 only | 4 |
| 1 and 2 | 5 |
| 1 and 3 | 6 |
| 1 and 4 | 7 |
| 2 and 3 | 8 |
| 2 and 4 | 9 |
| 3 and 4 | 10 |
| 1 and 2 and 3 | 11 |
| 1 and 2 and 4 | 12 |
| 1 and 3 and 4 | 13 |
| 2 and 3 and 4 | 14 |
| 1 and 2 and 3 and 4 | N/A |