# Answer 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?

This puzzle comes to me via the same source as the previous four. It also apparently appears in a book called 'Are You Smart Enough to Work at Google?'

Before reading the answer can I interest you in a clue?

The puzzle appears quite difficult. It's not dissimilar to the 'Die Hard Water Puzzle' but it is somewhat more complicated. Before we can take a run at it we're going to have to build some tools, we will then use them in combination.

Clearly though a better solution would be one that didn't require us to wait 7 minutes before we start. And there is a solution that allows this. We need to add 2 minutes on to the end of the 7 minute hourglass. Since the twice-flipped 4 minute hourglass will stop at 8 minutes we can flip our 7 minute hour glass here for the second time. At this point it will have been running for 1 minute, we will flip 1 minute's worth of sand back to the top and it will run for another 1 minute. This will total 9 minutes. As shown:

Not sure how to rate this for difficulty. When you have the solution in front of you it's almost trivial. But prior to that it seems very hard.

Personally I don't think the AI's explained this as succinctly as I did.

If you're curious what

If you're curious what

The puzzle appears quite difficult. It's not dissimilar to the 'Die Hard Water Puzzle' but it is somewhat more complicated. Before we can take a run at it we're going to have to build some tools, we will then use them in combination.

## 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.## Bringing it together

We already have a solution. It's most of the way there in the 'Difference' section above. We said if we start them both together and flip the 4 minute hourglass every time it runs out the difference between the 7 minute hourglass ending and the and the 4 minute hourglass ending for the second time is 1 minute. We just then need to flip it two more times to get 9 minutes. As shown:Clearly though a better solution would be one that didn't require us to wait 7 minutes before we start. And there is a solution that allows this. We need to add 2 minutes on to the end of the 7 minute hourglass. Since the twice-flipped 4 minute hourglass will stop at 8 minutes we can flip our 7 minute hour glass here for the second time. At this point it will have been running for 1 minute, we will flip 1 minute's worth of sand back to the top and it will run for another 1 minute. This will total 9 minutes. As shown:

Not sure how to rate this for difficulty. When you have the solution in front of you it's almost trivial. But prior to that it seems very hard.

Personally I don't think the AI's explained this as succinctly as I did.

If you're curious what

**Bard**made of this puzzle...If you're curious what

**ChatGPT**made of this puzzle...© Nigel Coldwell 2004 - – The

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