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Return to Treasure Island (Posted on 2012-04-05) Difficulty: 3 of 5

'Arr, ' said Long John Silver, 'Arr, arr,' by way of clearing his throat, before addressing his 9 remaining companions.

'We've sailed the seas for 7 long years, and plundered a pirate hoard, and the time has come to divvy the loot at last. It goes without saying that each of you lubbers wants all the treasure he can lay his hands on.'

'Now, as ye know, the Rules of the Sea require that the Captain shall propose a division, and all then vote, democratical-like; if the proposal be passed, then all take accordingly. If the lots cast be tied, the Captain votes again, to break the tie. But if the division be rejected, the Captain forfeits his share, and the right to propose passes to the next in rank, and so on until a division be agreed at last.'

Now gather round me hearties, and listen to me proposal, according to rank:

Long John Silver, Cook and Captain: 75 shares
Abe the Master: 1 share.
Ben the Mate: 1 share
Caleb the Gunner: 1 share
Dave the Able: 1 share
Eben the Bosun: 1 share
Fergus the Feeble: 2 shares
Gabe the Gimpy: 4 shares
Ham the Hopeless: 6 shares
Jesse the Cabinperson: 8 shares

'I'm sure you'll agree, lads, I've done you all proud.'

Of course, it's endlessly debatable whether Long John's proposal is fair; but should his proposal be carried, or not?

No Solution Yet Submitted by broll    
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Solution Fair? | Comment 13 of 14 |
Working backward through proposals...

Proposal                    "Captain"  Ayes  Nays
0 100                        Ham       1+1 > 1
1  0 99                      Gabe        2 > 1
2  0  0 98                   Fergus    2+1 > 2
3  1  0  0 96                Eben        3 > 2
4  2  0  0  0 94             Dave      3+1 > 3
5  3  1  0  0  0 91          Caleb       4 > 3
6  4  2  0  0  0  0 88       Ben       4+1 > 4
7  5  3  1  0  0  0  0 84    Abe         5 > 4
8  6  4  2  0  0  0  0  0 80 LJS       5+1 > 5
J  H  G  F  E  D  C  B  A

In the above proposal of LJS, no salt who is awarded more than 0 shares can insure his lot is improved or even stays the same, thus it should pass. As Ben, Caleb, Dave and Eben would get 0 shares, they each would vote for a proposal of:
0  0  0  0  1  1  1  1  0 96 LJS       5+1 > 5
And the proposal should also pass.
It is thus, the combined proposal as given by the Captain:
8  6  4  2  1  1  1  1  1 75 LJS
with a generous award of 1 share to Abe should garnish a near unanimous vote (Abe being unsatisifed with nothing less than 84 shares).
  Posted by Dej Mar on 2012-04-07 05:19:49
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