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sand clocks

How can you measure 9 minutes with a 7-minute hourglass and a 4-minute hourglass?

Note: In this question it states where it's possible or not but not the actual procedure for this exact situation.

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  • $\begingroup$ @athin it might! If it does, it probably says it in the first spoiler block of the accepted answer, I think. Maybe. Who knows? Not me, but I only tried to make sense of it for a minute or so. $\endgroup$
    – Bass
    Apr 10, 2020 at 0:32
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    $\begingroup$ @athin please see the note I added to the question. $\endgroup$ Apr 10, 2020 at 1:37

2 Answers 2

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Start both glasses. When the four-minute glass ends, flip it. When the seven-minute glass ends, flip it. When the four-minute glass ends again, flip the seven-minute glass. When the seven-minute glass ends again, that's nine minutes total.

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We start the hourglasses at the same time. When the 4-minute hourglass stops we turn it to the other side. The 7minute hourglass will have three more minutes to stop, so when it stops we turn it to the other side and in the meanwhile the 4minute one will have 1 more minute to stop. When the 4minute one stops we turn it to the other side and in the meanwhile the 7minute hourglass will need 6 minutes to stop. When the 4minute hourglass stops the 7minute one will need 2 minutes to stop. We start measuring from this time the 2 minutes to stop and we turn it to the other side for the rest 7 minutes.

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    $\begingroup$ While this solution definitely works, msh210's solution measures the 9 minutes starting from the first timer flip, so I'd say it must be the correct answer; this solution takes a long preparation time before we get to the actual measurement. $\endgroup$
    – Bass
    Apr 10, 2020 at 0:49

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