## A cup conundrum

By Ariel Marcy, 26 July 2023

**Difficulty: Tricky**

Fernando has 3 water-tight containers that measure 3 cups, 9 cups, and 20 cups (for brevity, these are referred to as C3, C9, and C20, respectively).

The containers have no markings to indicate other volumes, so there’s no way to know when a container is, say, half full. The containers have nice spouts, so they’re easy to pour between without spills or drips, and it’s easy to tell when they are completely full so you can stop pouring.

Using only these containers, a water tap and a drain, how can Fernando measure: a) 12 cups, b) 6 cups, c) 2 cups, d) 1 cup?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

Get creative with how you can add and subtract volumes! For example, to measure 8 cups, Fernando fills the C20 and then pours exactly 9 cups into the C9, leaving 11 cups in the C20. He then pours exactly 3 cups into the C3, leaving 8 cups in the C20.

## Brainteaser answer

Here are some of the shortest methods, but there are plenty of different ways to solve each of these problems!

a) Fernando fills C3 and C9 and pours them into C20 to make 12 cups.

b) Fernando fills C9, pours exactly three cups into C3, leaving 6 cups in the C9.

c) Fernando fills C20, pours exactly nine cups into C9 and then empties the C9. From the C20, he pours exactly 9 cups into the C9 again, leaving 2 cups in the C20.

d) Fernando fills the C9, pouring it into the C20. He repeats the process so that there are 18 cups in the C20. He then fills the C3 and pours it into the C20 until the C20 is full, leaving 1 cup in the C3.

If you liked these problems, it is possible to find a solution for 1 through 20 cups of water. Challenge yourself to come up with all 20! And while you’re at it, pop your solutions in the comments.

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