Puzzle: Marbles

[Bungleau]

There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times. How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings?

[VulcanRider]

Originally posted by Bungleau: There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times. How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings?

Weigh marbles 1,2,3 vs. 4,5,6. If they're equal, than the heavier one is either 7 or 8. Weigh 7 vs 8 and take the heavier one.

If 1,2,3 vs 4,5,6 is not equal, take the heavier group. Say it's 1,2,3. Now weigh 1 vs 2 and take the heavier one. If they're equal, it's 3.

Try this one: You've got a 4 minute hourglass and a 7 minute hourglass. How do you measure exactly 9 minutes?

[sageridder]

Take the tops off both dump the sand out of the 4 min one.Pour sand from 7 min one into the empty 4 min one.Throw 4 min one at someone.The 7 min one now has 3 min of sand,put top back on and flip three times to measure 9 min.

[sylent]

lol, is the sandthrowing part important? [img]tongue.gif[/img]

Looks like we've got some good logical thinkers, that sort of thing is usually lost on me though

[VulcanRider]

Originally posted by sageridder: Take the tops off both dump the sand out of the 4 min one.Pour sand from 7 min one into the empty 4 min one.Throw 4 min one at someone.The 7 min one now has 3 min of sand,put top back on and flip three times to measure 9 min.

Ok, now THAT'S what I call thinking outside the box. But can you do it another way?

[Cerek the Barbaric]

Turn the 7 minute hour glass over. When the sand runs to the bottom, take the 4-minute hourglass and set it at a 45degree angle. That should allow only half the sand to run to the bottom - which will cover the 2 extra minutes.

[andrewas]

I dunno if that would work. Hourglasses are shaped so most of the sand would fall trough at 45 degree.

Anyway, my solution.

Turn over the seven and the four. When the four runs out, flip it. When the seven runs out, stop the four. You now have one minute in the four. Run the seven for one minute. You now have six minutes left on the seven.

Run the four and the seven to get two minutes remaining in the seven. Run the four and the seven again to get two minutes remaining in the four. You now have a four minute hourglass with two minutes in it, and a seven minute hourglass with seven minutes in it. Run those one after the other, and you have nine minutes.

EDIT] My previous solution was more elegant, because I was using the wrong numbers.

[ 02-21-2003, 03:30 PM: Message edited by: andrewas ]

[Cerek the Barbaric]

Good answer, andrewas. [img]graemlins/thumbsup.gif[/img] The only drawback is that it takes 14 minutes to prepare the hourglasses to measure the 9 minutes. [img]graemlins/verysad.gif[/img]

New Solution: This is the 21st Century! Stop fooling around with hourglasses and buy a STOPWATCH! {yeesh}.

[Bungleau]

Jeez... it's a bummer for the first response to be the correct one. Thought I'd found a tricky one... guess not.

But let me respond back...

Start both hourglasses. When the four-minute hourglass is empty, flip it. Elapsed time four minutes, and three minutes worth of sand left in the seven minute hourglass.

When the seven minute hourglass is empty, flip both. Incremental time is three minutes, for an elapsed time of seven minutes. One minute of sand left in the four minute hourglass, and seven minutes in the now-flipped seven minute hourglass.

When the four minute hourglass empties, flip the seven minute hourglass. Incremental time is one minute, for a total of eight minutes. Seven minute hourglass now has one minute of sand on top, and six on the bottom.

When the seven minute hourglass is empty, you will be at nine minutes.

[VulcanRider]

Originally posted by Bungleau: When the seven minute hourglass is empty, you will be at nine minutes.

Very good. Try this one:

A businessman had an important meeting that required him to fly by Concorde from London to New York. That morning, his wife drove him to the airport & saw him off at the gate. She watched his plane take off, then went back to her car.

The Concorde is a direct flight -- no stops. Yet when he arrived in New York, she was there to pick him up. How is this possible using current technology (no "Beam me up, Scotty") ??