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100 Day Challenge 2020

Don't Waste Water!

Two containers: one holds 33 liters and the other holds 5.5.

The challenge: measure a specific quantity of liquid using only a sequence of actions chosen from the legal moves below.

We can use these moves to measure amounts of water that are different from the exact measurements on the bottles. For example, if we fill the 55-liter container and pour it into the 33-liter container until it is full, we can be certain that we have 22 liters remaining in the larger bottle.

We can also combine multiple steps to find even more measurements. For example, we can measure out 11 liter by doing the following:

  1. Fill the 33-liter bottle.
  2. Empty the 33-liter bottle into the 55-liter bottle.
  3. Refill the 33-liter bottle.
  4. Pour the 33-liter bottle into the 55-liter bottle until the larger bottle is full.

This leaves us with exactly 11 liter left in the smaller bottle.

Today's Challenge

You have one container that holds 44 liters and another container that holds 77 liters.

These are the only moves possible:

  • Completely fill a container from the tap.
  • Completely empty a container onto the ground.
  • Pour a container into another until one is completely full or the other is completely empty.

Using only the moves listed above, what is the smallest amount of water you need to pour onto the ground in order to measure 22 liters in either one of the containers?

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