Math Is Fun Forum

LaughingMan_dD

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5 pirates version 2

The solution given for the 5 pirates version 2 in the logic puzzles section is wrong. Not exactly wrong, but here 2 perspectives were possible!
so this is how site's answer goes:
Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie....
Working backwards:

2 Pirates: Duncan splits the coins 0: 100 (giving all to Eddie). Otherwise, and perhaps even then, Eddie would vote against him and over he goes!

3 Pirates: Colin splits the coins 99 : 1 : 0. Eddie is going to vote against him no matter what (see above) so gets nothing, but Duncan will vote for him, to get at least one gold out of it (if Duncan votes against him, there will only be two pirates remaining and Duncan will get nothing, and may even lose his life!)
Okeh.. here comes the diversion to the perspectives.. 1st perspective is what is given In the original solution, and the answer turns out to be 97:0:1:0:2
Okeh, now for 2nd perspective.. see.. in the original answer in 4th stage when billy turned in he devided the money as 97:0:2:1
And duncan and eddie accepted the deal assuming that they will get more than before.. yeah definitely eddie gets more than before, but duncan's decision is ambigous! Because billy and collin both are trying to please duncan consequtively, to get his vote(where as in eddie's case only billy is trying to please him!)
since billy and collin both are tryin to please him, it wouldnt be right to assume that in future if billy dies and 3rd stage arrives then collin will give him only 1 pence.. because of the ambiguity i explained above!  it was possible in 3rd case maybe collin was thinking of giving 3 pence! After all collin and duncan are not instant enemies(as against duncan and eddie)..
Duncan can in no way quantitatively judge who will give him more pence, collin or billy? And since Duncan is a blood thirsty naughty(like other pirates) he will most probably try to kill the most number as possible, so it is equally likely that duncan will vote against billy! Now we already know what happens if duncan votes for billy(as given in site's answer) so lets speculate what would happen if duncan votes against billy, it would mean billy has the possibility to die!
So now, when 5th stage arrives:
5 pirates: alex devides the coins as 98:1:0:0:1
billy will vote (because its 2nd perspective and i already explained it)
eddie will also vote because if alex dies, billy dies and in collin's case he gets a 0!!
See... so 2 possible aswers were possible all because duncan's decision got an ambiguity.. we cant say giving duncan a 2 pence by billy will satisfy him.. since collin also is trying to please duncan and also he is not his instant enemy(in ver. 1 [also in logics section]collin was duncan's instant enemy... billy was collin's instant enemy and all..)
so logically there is no.guarrantee that duncan will vote for billy.....
at the same time duncan can vote for billy assuming he gets more pence, but think if actually such a situation comes forth wont collin and billy bargain increasing each penny? (Eg. Collin can say duncan to vote against billy instead he(collin) will give more than 2 penny.. like an oath or promise among pirates? It wasnt really necessary that in 3rd case collin would give him only 2 pence!)
yeah i can gurantee 1 thing... if the pirates are not business minded then yeah site's answer will come out to be correct... but that would just mean those pirates are not intelligent! and yet they are quite intelligent... think about it... these are the 2 perspectives i meant!
That question would have been better if ver. 2 was not made!

i just started this thread to explain something with relevance to my previous thread "5 pirates puzzle ver.2"
i wanted to explain what i meant by "instant enemies"
see.. in that puzzle if a pirate feels 'its better for me if this person did not exist' then that 'this person' is his instant enemy, that is what i meant.. eg. In ver. 1 collin was duncan's instant enemy and billy was collin's since in billy's absense collin got 99 pence but in presence he gets 0 pence.. similarly in collin's absense duncan got 99 pence but in presence only 0.. the difference in their gains is extremely high!
but in ver.2 thats not true.. in billy's presence and absence the difference of money duncan gets is only 1 pence.. so billy or collin neithet of them is duncan's instant enemy.. and since 2 consequtively old pirates came into scene who are not duncan's instant enemies.. that is wha makes duncan's decision ambigous!