Two Glasses of Water

Jan 23, 2021

RAY: This puzzler was sent in by Frank Juskolka. Frank writes: You have a four-ounce glass and a nine-ounce glass. You have an endless supply of water. You can fill or dump either glass.

It turns out, you can measure six ounces of water using these two glasses. The question is:

How many steps are involved and what's the fewest number of steps in which you can measure six ounces?



RAY: Start with both glasses empty. Step one, you fill the nine-ounce glass. Step two, you pour four ounces from the nine-ounce glass into the four-ounce glass because that's all you can do. Step three, you dump out the four-ounce glass. Now you’ve got five ounces left in the big glass.

Step four, again you fill the four-ounce glass from the nine-ounce glass. And step five, again dump the four-ounce glass. So now the four-ounce glass is empty, and you’ve got one ounce in the nine-ounce glass.

Step six, pour the one ounce of water from the nine-ounce glass into the four-ounce glass. Step seven, fill the nine-ounce glass.

So at the moment here you've got a full nine-ounce glass, and you have one ounce in the four-ounce glass.

So now you pour just enough water from the nine-ounce glass to fill the four-ounce glass. Which means you're pouring how much out of the nine-ounce glass?

Three ounces, right, and that leaves how many ounces in the nine-ounce glass?



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