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Arithmetic Puzzles

Arithmetic puzzles are Mad Libs for math: fill in the blanks with numbers or operations to make the equation true.

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You have a container that holds 3 liters and another that holds 5 liters. If you repeatedly fill the 3 liter container completely and completely pour it into the 5 liter container until the 5 liter container is full, how many liters will be left in the 3 liter container at the conclusion of this process?


Assume you have access to a large well that holds as much water as you need. You can pour water into, out of, or between your containers as many times as you want. However, your containers have no measurement markings, so you can't know how much you are pouring unless you are completely emptying or completely filling a container.

You have a container that holds 3 liters and a container that holds 5 liters. You want to measure 4 liters by using the following strategy:

Fill the 3 liter container completely and completely pour it into the 5 liter container. Repeat this process until the 5 liter container is full, then empty it. Pour any remaining liquid in the 3 liter container into the 5 liter container, then start this entire process again.

How many times during this entire process do you have to fill the 3 liter container from the well?


Assume you have access to a large well that holds as much water as you need. You can pour water into, out of, or between your containers as many times as you want. However, your containers have no measurement markings, so you can't know how much you are pouring unless you are completely emptying or completely filling a container.

You have a container that holds 4 liters and a container that holds 6 liters. You want to measure 5 liters by using the following strategy:

Fill the 4 liter container completely and completely pour it into the 6 liter container. Repeat this process until the 6 liter container is full, then empty it. Pour any remaining liquid in the 4 liter container into the 6 liter container, then start this entire process again.

How many times during this process do you have to fill the 4 liter container from the well?


Assume you have access to a large well that holds as much water as you need. You can pour water into, out of, or between your containers as many times as you want. However, your containers have no measurement markings, so you can't know how much you are pouring unless you are completely emptying or completely filling a container.

You have a container that holds 6 liters and another container that holds 9 liters.

Is it possible for you to measure every whole number of liters between 1 and 15 using just these two containers?


Assume you have access to a large well that holds as much water as you need. You can pour water into, out of, or between your containers as many times as you want. However, your containers have no measurement markings, so you can't know how much you are pouring unless you are completely emptying or completely filling a container.

You have a container that holds 12 liters. You need to measure 7 liters.

What other size container should you take?


Assume you have access to a large well that holds as much water as you need. You can pour water into, out of, or between your containers as many times as you want. However, your containers have no measurement markings, so you can't know how much you are pouring unless you are completely emptying or completely filling a container.

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