**The ****C****hallenge **

**C**

*Difficulty: 1/5*

You arrive at the door to steal the bank blueprints, when you see Gary the guard.

“Do you have a drink?” he asks. “Guarding blueprints makes me so thirsty,”

He seems like a nice guy, but if you make him the perfect drink, perhaps you could put him to sleep for long enough to steal the blueprints.

You make your way to the bar and you see this:

The question is, which 3 bottles should you choose to make the perfect drink which will:

- Put Gary to sleep
- Won’t poison him
- Be perfectly balanced

**The Solution**

There are many ways to do this, but here we can proceed through *deduction*.

We have 3 “elements” per bottle, which means that **9 elements** will go into the draught in total. But we can only put 4 + 2 + 1 = **7 items** in total. To account for the remaining 2 elements, we can deduce that they must be sunflowers.

Because we need 2 sunflowers, **we must choose bottle F**. The only alternative way to obtain 2 sunflowers is choosing both bottles B and E – but neither of these are purple, and since we can only choose a total of 3 bottles, even if the remaining bottle were purple, we would still be left with an extra sunflower; an unbalanced result.

To balance the 2 sunflowers, the remaining 2 bottles must be purple so we must choose from A, C, D, and H. Since the recipe only calls for 1 snail shell, we can deduce that we need **bottle A **as this is the only bottle to have only one snail in it.

Finally, to balance the recipe, we can conclude that the remaining 2 monkeys and elephant can only come from bottle H, so the final answer is that we should choose A, F and H.

The benefit of deduction is that it becomes clear that there exists no other solution.

**Why is this algebra?**

Because we have a system of 8 linear equations (the 8 bottles) with 4 variables (monkey, elephant, snail, sunflower; note that a purple bottle is equivalent to ” – sunflower”).