[Guest]

Luke found this treasure map to an Island which holds a big chunk of treasure. He figured out the route to the place, but the rules to be followed to reach there and come back with the money confused him.

Here are the items to be noted to reach the treasure and come back with money:

1. He need to cross 5 different rivers. Boats are available to cross these rivers, but each boat man will take half of the total money that is with him at the moment.

2. Once he crossed all 5 rivers and reached the treasure island, the islanders will allow him to take the treasure in terms of Dollars ($$), but the total amount he can take back from the island cannot be more than 1 Million Dollars (inclusive of the money he has with him at the moment). For E.g. if he has $100,000 with him at the moment, he can take only $900,000 from the island.

3. To reach back to his place, he needs to cross those 5 rivers back and pay fees to the boat men in the same manner as mentioned in 1.

So, the questions here is:

A -- What is the Maximum profit Luke can ever bring home from the Island?

B -- How much money he should take from home to bring the maximum profit?

Good luck, and peace!

[Guest]

Since he doesn't HAVE to take money with him for the boatmen, take 0. This way, 0/2/2/2/2/2 = 0 lost. He can then take the full 1,000,000 from the stash. This will leave him with 1,000,000/2/2/2/2/2 = $31,250. Since you can only ever have 1,000,000 at one time, this is the maximum you can ever get out of the village. Likewise, any cash you bring is just wasted on the boatmen, and thus reduce you profits, since having money at the village does you no good, because then you take less.

[Guest]

Question

Does each boatman take the same fee to cross the river on the return as he did on the inital crossing or is it alway 1/2.

For example if I met the first boat man with only 2$ in my pocket the fee would be 1$. On my way back across would he still take 1$ or would he take half of what I currently had?

>>Nevermind, I believe I've found my answer.

Edited July 31, 2009 by KillerGuns

[Guest]

Since he doesn't HAVE to take money with him for the boatmen, take 0. This way, 0/2/2/2/2/2 = 0 lost. He can then take the full 1,000,000 from the stash. This will leave him with 1,000,000/2/2/2/2/2 = $31,250. Since you can only ever have 1,000,000 at one time, this is the maximum you can ever get out of the village. Likewise, any cash you bring is just wasted on the boatmen, and thus reduce you profits, since having money at the village does you no good, because then you take less.

Well. I should have been more clearer -- The boatmen wont do free service, and wont work if you pay them less than a Dollar. Sorry for the confusion!

[Guest]

A. 31,250,000$ can be brought back so Profit = 31,249,968$

B. 32$

Edited July 31, 2009 by KillerGuns

[Guest]

A. 31,250,000$ can be brought back so Profit = 31,249,999.68$

B. 0.32$

Sorry. Just added a reply on clear rule with boat men.

[Guest]

He starts out with $.032 and winds up getting $999,999.99 of treasure. He returns with $33,740.00 less his initial $0.32 = Total Profit of $ 33,749.68.

[Guest]

You need to start with 32 dollars.

First boatman takes 16 dollars, leaving you with 16

Second boatman takes 8 dollars leaving you with 8

Third takes 4 leaving you with 4

Fourth takes 2, leaving you with 2

Fifth takes 1, leaving you with 1. Note that since the last boatman takes at least a dollar, you need 2 times as much at this point.

SO you have $1, and get $999,999 on the island. You now have 1 million dollars.

Fifth takes 500,000 leaving you with 500,000

Fourth takes 250,000

and so on.

At the end you have a total of $31,250. On the way out, you spent $31. On the way back you spent 968,750. You received 999,999. Your profit therefore is $31,218.

[Guest]

You need to start with 32 dollars.

First boatman takes 16 dollars, leaving you with 16

Second boatman takes 8 dollars leaving you with 8

Third takes 4 leaving you with 4

Fourth takes 2, leaving you with 2

Fifth takes 1, leaving you with 1. Note that since the last boatman takes at least a dollar, you need 2 times as much at this point.

SO you have $1, and get $999,999 on the island. You now have 1 million dollars.

Fifth takes 500,000 leaving you with 500,000

Fourth takes 250,000

and so on.

At the end you have a total of $31,250. On the way out, you spent $31. On the way back you spent 968,750. You received 999,999. Your profit therefore is $31,218.

Absolutely. Not only did I not read the requirement for the dollar written out longhand instead of $1.00, but I can't divide either!!

Given a mental fix on those two things, my method was correct.