# Hint to Puzzle #40: 4 & 7 minute hourglasses to measure 9 minutes

40. Using only a 4 minute and 7 minute hourglass or egg timer how would you measure exactly 9 minutes?

The best way to approach this is to build the tools you need to solve the puzzle. The section below is an extract from the answer.

## Addition

The simplest of our tools. We can combine hourglasses in series. We could use the 4 and the 7 one after the other to measure 11 minutes. Or any other simple combination.## Difference

If we were to start both hourglasses together, flip the 4 when it reaches the end the difference between it ending for the second time and the 7 minute ending is 1 minute. The difference between 4 runs of the 4 and 3 runs of the 7 would be 16 as against 21 respectively. So 5 minutes.## Early flipping

We could for example start both timers together. When the 4 minute hourglass runs out we know that the 7 minute hourglass has run for 4 minutes also and so must have 4 minutes of sand in the bottom. If we flip it now it will necessarily run for 4 minutes.There's more than one answer here but some are better than others.

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