Fun brainteaser

[Lotan]

You have two hourglasses. One empties in 7 minutes.

The other empties in 4 minutes.

How can you use these two hourglasses to measure exactly 9 minutes?

 

[Katzenfreund]

A good one to get this old cat to use his brain again. Thanks.

To avoid spoiling for the others, I use a spoiler. EDIT: but which doesn't seem to work, so I've moved the solution further down.


















A = 7 mins
B = 4 mins

Start (reverse) them both
When B empties (in 4 mins), A has 3 mins left
Start the count and reverse B
In 3 mins: A empties, B has emptied by 3 mins (has 1 min left)
Reverse them both. Now A has 7 mins and B 3 mins
In another 3 mins: B empties and A has emptied by 3 mins
Reverse A
In 3 more mins (total 9 mins): A empties.

QED

 

[wotw]

A = 7 mins
B = 4 mins

Start both
When B empties (4 mins), A has 3 mins left
Immediately reverse B
In 3 mins: A is empty and B has emptied by 3 mins (has 1 min left)
Immediately reverse A.
When B empties again, A has flowed back by 1 min (now a total of 8 minutes)
Reverse A again
In 1 min (total 9 mins) A again empties.

Lots of Cheer - wotw