Word Problems

Three surgeons and a clumsy cook go camping in the remote wilderness. The clumsy cook stumbles over the campfire as he is serving the surgeons, injuring himself and dumping hot stew on the hands of the surgeons. The cook’s injuries need surgical treatment. The surgeons’ injuries are minor but open. It turns out they brought the equipment necessary for the cook’s surgery with them, and they can use the campfire to sterilize the tools. But there are only two pairs of rubber gloves. Because of the different surgeons’ skills, all three of the surgeons are needed to operate on the cook, in sequence. How can this be done without any of them being exposed to the blood of any of the others?

Another one:

You have a jug that holds five gallons, and a jug that holds three gallons. You have no other containers, and there are no markings on the jugs. You need to obtain exactly seven gallons of water from a faucet. How can you do it?

Second Problem: You need exactly four gallons. Using the same two jugs, describe two ways of going about doing this.

ImaniOU’s first jug:

Fill the 5-gallon jug and pour it into the 3-gallon jug. You’ll have 2 gallons left in the 5-gallon jug. Empty the 3-gallon jug and then pour the 2 gallons from the 5-gallon jug into the 3-gallon jug. Then fill the 5-gallon jug from the faucet again and you’ll have a total of 7 gallons.

[mod’s note: Highlight above to view jeff’s solution]

Okay, jeff…now try the second part of the solution. One answer is really common, the other I made up and have not seen it appear anywhere (and it involves one less step than the more common one).

Alright ImaniOU, first I’d say “what’s this ‘gallon’ bullshit? The world went metric decades ago didn’t it?” Then I’d find a 5 litre jug, a 2 litre jug and a tap. Then…

Fill the 3L jug, pour into the 5, fillt he 3 again, and pour into the 5, leaving 1L in the 3. Empty the 5, throw the 1L in it. Pour 3 more litres in the 5. Fill the 3, and use this to top up the 5, which would leave 2L in the 3. I’ve got 7L. The second problem must be much the same.


ImanIOU’s 2nd jug:

[color=white]Fill the 3-gallon jug and pour it into the 5-gallon jug. Fill the 3-gallon jug again and pour into the 5. You’ll have 1 gallon left in the 3-gallon jug. Empty the 5-gallon and add the remaining 1 gallon from the 3-gallon jug. Fill the 3-gallon jug and empty it into the 5-gallon jug to get 4 gallons.


Pour the 5-gallon into the 3-gallon jug, leaving 2 gallons in the 5-gallon jug. Empty the 3-gallon jug and dump the remaining 2 gallons into it. Fill the 5-gallon jug again and pour 1 gallon of it into the 3-gallon jug, filling the 3-gallon jug and leaving 4 gallons in the 5-gallon jug. Sorry, I don’t know how to do the spoiler font[/color]

Right, Jeff’s method is so simple, it seems unnecessary to think of another one, but this works too and is almost as quick:

Fill the 5L jug and empty it into the 3L jug. You’ve now got 2L left in the 5. Empty the 3, and pour your 2L from the 5 to the 3. Fill the 5 again and then use it to top up the 3L. You’ll then have 4L left in the 5.