# Hourglasses 2 Puzzle - Solution

### The Puzzle:

An eccentric professor used a unique way to measure time for a test lasting 15 minutes.

He used just two hourglasses. One measured 7 minutes and the other 11 minutes.

During the whole time he turned the hourglasses only 3 times.

How did he measure the 15 minutes?

He used just two hourglasses. One measured 7 minutes and the other 11 minutes.

During the whole time he turned the hourglasses only 3 times.

How did he measure the 15 minutes?

### Our Solution:

When the test began, the professor started both hourglasses running.

When the 7min hourglass ran out, he turned it around.

4 minutes later, the 11min hourglass ran out, and he promptly turned the 7min hourglass around again, so the 4 min ran back again.

11+4=15, and the test was over.

Footnote: Dr. J Sreedhar wrote to tell me that the Prof could have done it with one less flip:

* Start both (11-min and 7-min) hourglasses, but not the test.

* When the smaller one runs out, start the test. The bigger hourglass has 4 min to go.

* When the bigger hourglass also runs out, just flip it to measure out 11 more min.

* Test is over when the bigger hourglass runs out for the 2nd time.

When the 7min hourglass ran out, he turned it around.

4 minutes later, the 11min hourglass ran out, and he promptly turned the 7min hourglass around again, so the 4 min ran back again.

11+4=15, and the test was over.

Footnote: Dr. J Sreedhar wrote to tell me that the Prof could have done it with one less flip:

* Start both (11-min and 7-min) hourglasses, but not the test.

* When the smaller one runs out, start the test. The bigger hourglass has 4 min to go.

* When the bigger hourglass also runs out, just flip it to measure out 11 more min.

* Test is over when the bigger hourglass runs out for the 2nd time.

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