[rookie1ja]

Hourglass I. - Back to the Water and Weighing Puzzles
Having 2 sand-glasses: one 7-minute and the second one 4-minute, how can you correctly time 9 minutes?

Spoiler for Solution:

Sand-Glass I. - solution
Turn both sand-glasses. After 4 minutes turn upside down the 4-min sand-glass. When the 7-min sand-glass spills the last grain, turn the 7-min upside down. Then you have 1 minute in the 4-min sand-glass left and after spilling everything, in the 7-min sand-glass there will be 1 minute of sand down (already spilt). Turn the 7-min sand-glass upside down and let the 1 minute go back. And that's it. 4 + 3 + 1 + 1 = 9

[metallicats]

You can correctly time 9 minutes by repeatedly flipping over the two glasses in this order:
each 1 stands for a minute and ** stands for flip

1 1 1 1*1 1 1 1*1 1 1 1*1 1 1 1*1 1 1 1
*********1 1 1 1 1 1 1*1 1 1 1 1 1 1

once the one seven minute glass is done, there is only one minute left in the four minute glass. two more flips of the four minute glass will get you nine minutes. To make it easier, start the four minute glass and when it's half full flip the seven minute glass.

[mannu]

I think there is a faster way to do this..

Start with both the hr glsses. At the end of 4 minutes keep the 4min glass inverted and wait for the 7min hr glass to get empty. When the 7min glass is empty keep it in inverted position. After 1 minute, totally 8 minutes have passed. Now invert the 7min hr glass. And u have 4 + 4 + 1 =9.

Tell me if its not right.

[peachykeen]

I think I have something that could work...

Turn both glasses over and let them run. Once the 4 min is done, turn it over again and let it run until the 7 minute glass is done. Once the 7 minute glass is done, there is one minute left on the 4 minute glass, so turn it over to let the one minute run through and this begins the 9 minutes you are timing. Then just turn the 4 minute over two more times to gain the 8 more minutes you need to get a total of 9 minutes.

[imagoombah]

Although, peachykeen, yours is the only answer anyone can understand, nine min. could be timed a bit faster using a similar method.

-Start both timers

1. When the 4 min. glass is done, start it again. (The 7 min. glass now has 3 min. left to count)

2. When the 7 min. glass is done, start it again. (There will be one min. remaining on the 4 min. glass and the 7 min. glass will now be counting that one min.)

3. When the 4 min. glass is done, the 7 min. glass will now have just one min. worth of sand on the bottom, turn it over and that sand will count the remaining min.

1. 4min. (from the 4 min. glass)
2. 3min. (from the 7 min. glass)
3. 1min. + 1min. (the first from the 4 min. glass, the second from the 7 min. glass)

[Aseatha85]

there is a much simpler meathod.

it says corectly time 9 mins with the two glasses, it never says you have to use them at the same time.

so start the 4 min glass, when that is half gone, start the 7 min glass

2+7=9

much faster and much less hassle then to stand there and flip the glasses several times.

[peachykeen]

Quote

there is a much simpler meathod.

it says corectly time 9 mins with the two glasses, it never says you have to use them at the same time.

so start the 4 min glass, when that is half gone, start the 7 min glass

2+7=9

much faster and much less hassle then to stand there and flip the glasses several times.

It would be easier, but there is no way to tell that you are timing exactly 9 minutes because you cant, by sight, get the exact half way point of the 4 minute glass.

[cpotting]

Several people, so far, have commented on having "faster" ways to solve this problem.

I'd just like to point out, that ALL these methods take 9 minutes. None of them are "faster".

pedantic, but true

[firefox]

4min---|--7min|Time
---------------------
down-4|down-7|0
up-4---|down-3|4
up-1---|up-7---|7
down-4|up-6---|8mins

In sand glasses we can count to the minute mentioned or for each inversion. So I don't think
4+3+1+1 =9 will work because we can't measure the last minute.Please point out if I'm wrong in this regard.

A probable solution will be
4min---|--7min| Time
---------------------------
down-4|*****| 0
up-4 --|down-7| 4
down-4|down-3| 8
up-1---|down-0| 9mins

4+4+1=9 .

P.S: Note that in both the tables the time is taken into account only if there is an inversion (down-up or up-down) of either of the sand glass in use.And ***** is used to indicate not needed, | is used as a separator....corrected one...

thanks,
firefox...

[zhuazi]

a b

4/0 7/0
0/4 3/4 flip a
4/0 3/4 time begin
3min
1/3 0/7 flip a b
3/1 7/0
3min
0/4 4/3 flip b
3/4
3min

3+3+3=9 min