Hint to Puzzle #40: 4 & 7 minute hourglasses to measure 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.
AdditionThe 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.
DifferenceIf 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 flippingWe 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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