# What proposal should elf Ee make ?

183 views

There was once a troop of 5 elves. The 5 elves were very dedicated on finding the magical treasure of 1000 coins. However, being elves, they were super geniuses, very greedy and they did not hesitate in taking lives of other elves. The 5 elves were named Aye, Bee, Cee, Dee and Ee, ranked from high to low respectively, from Aye to Ee. One fine day, their efforts brought results and they found 1000 coins. Now they had to split it in between them as per their ranks. The lowest ranked elf has to make the proposal. If the proposal is accepted by majority, it is agreed, or the suggesting elf is killed.

What proposal should elf Ee make ?

posted Sep 4, 2015

The elf Ee should give 997 coins to himself, 2 coins to either Elf Aye or Bee, and 1 coin to Cee.
Here, we derive the solution working backwards.
If only elf Aye and Bee are left, Aye will reject all proposals from Bee, since elves are greed and killers, as Aye gets to keep all 1000 coins.
However, if Cee was alive, and would give 1000 coins all to himself, even then Bee would agree since If he does not, Cee dies, and as we have seen, if only Aye and Bee are left, Bee will be killed. So the vote is Aye: No, Bee and Cee, yes.
Now if Dee was alive, he would propose to give 1 coin to Aye, 1 to Bee, none to Cee and 998 to himself. Aye and Bee will agree to this, because if they dont, Dee will die and Cee will get to keep all 1000 coins. Since they are greedy, and would prefer 1 coin over none, they will agree to this proposal.
However, elf Ee should give 2 coins to Aye (so he will agree as he gets 1 extra coin over the previous proposal). He will give 0 coins to Bee. He shall give 1 coin to Cee (and Cee will agree since in the previous proposal, Cee was getting nothing). He will give Dee 0 coins so D will disagree. Obviously, Ee gives himself 997 coins. The vote is 3 yes, two nos. Thus Ee will propose this.

answer Sep 21, 2017

To save his life, Ee will need to keep 0 coins for himself

4x + 3x + 2x + x= 1000

10x = 1000

x=100

Aye= 400,
Bee= 300,
Cee= 200
Dee=100
Ee=0

answer Aug 7, 2020 by anonymous
–1 vote

Aaa takes 202, Bee takes 201, Cee takes 200, Dee takes 199, Ee takes 198

answer Sep 16, 2015 by anonymous

Similar Puzzles

A pirate ship captures a treasure of 1000 golden coins.
The treasure has to be split among the five pirates: 1, 2, 3, 4, and 5 in order of rank.

The pirates have the following important characteristics:

• Infinitely smart.
• Bloodthirsty.
• Greedy.

Starting with pirate 5, they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it.

An innocent person is accused of a murder in a village. The head of the village knows that the man is innocent but he also knows that the truth may be uncovered one day that his own son is the murderer. Just to hinder the attention of people, he offers a chance to the man. In a jar, he places two chits of paper – one reads innocent and the other reads guilty. Among all the other villagers, he asks the accused person to pick up a chit. He says that their almighty god is watching them and the person will meet his fate truthfully with the chit.

Of course, the village head is cheating. He has put both chits with Guilty written on them. The accused person somehow suspects the same. But no one will believe him if he tries to expose the head. Also, he knows no one will look at the other chit once his fate is decided by his selected chit.

What should he do to prove that he is innocent?

A man get trapped in a psycho's mansion during a power outage. He tries to get out by going through a series of rooms: the first one is red, the second one is also blue, but the third one is golden. After he go through all of these rooms he find the psycho. The psycho tells him that he must hold your breathe under water for 10 minutes, wrestle a large bear, or sit in the electric chair for ten seconds while it is on.

Which should the man choose?