# Hourglasses

#### Alexmahone

##### Active member
Bob owns a couple of hourglasses -- one is a 4 minute hourglass and the other is a 7 minute hourglass. If Bob wants to measure 9 minutes, how could he do it?

#### CaptainBlack

##### Well-known member
Bob owns a couple of hourglasses -- one is a 4 minute hourglass and the other is a 7 minute hourglass. If Bob wants to measure 9 minutes, how could he do it?
Start then together, turn the 4 when it is emply. When the 7 is empty start timing the nine minutes, at this point the four minute glass has 1 minute to go. When empty turn it, 5 minutes have elapsed. Turn it again, and when empty 9 minutes have elapled.

CB

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#### Alexmahone

##### Active member
Start then together, turn the 4 when it is emply.
Now there are 3 minutes remaining in the 7.

When the 7 is empty turn the 4.
When the 7 is empty there is 1 minute remaining in the 4. So why would you want to turn it?

At this point it has 1 minute to go...

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#### CaptainBlack

##### Well-known member
Now there are 3 minutes remaining in the 7.

When the 7 is empty there is 1 minute remaining in the 4. So why would you want to turn it?
Typo, now corrected (I hope)

CB

#### Alexmahone

##### Active member
Start then together, turn the 4 when it is emply. When the 7 is empty start timing the nine minutes, at this point the four minute glass has 1 minute to go. When empty turn it, 5 minutes have elapsed. Turn it again, and when empty 9 minutes have elapled.

CB
Okay, that works but it's a little inefficient as it wastes the first 7 minutes. There's a better solution.

#### Alexmahone

##### Active member
Hint: There is a solution that wastes no time and measures 9 minutes in one go.

#### conscipost

##### Member
Start the two together. When the four is empty, flip it (four minutes elapsed). When the seven is empty, flip it (7 minutes). When the four is empty again flip the seven (8 minutes). Wait then the remaining minute for the seven to empty.

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#### oasi

##### New member
Hint: There is a solution that wastes no time and measures 9 minutes in one go.
yes +1