test your intelligence
stop slacking and let your brain do some work... some say this is a pri. 5 mathematics problem.
5 pirates on an island have 100 gold coins to split among themselves. They divide the loot as follows: The senior pirate proposes a division and everyone votes on it. Provided at least half the pirates vote for the proposal, they split the coins that way. If not, they kill the senior pirate and start over. The next most senior (surviving) pirate then proposes his own division plan, and they vote by the same rules and either divide the loot or kill the senior pirate, as the case may be. The process continues until one plan is accepted.
Suppose you are the most senior pirate. What division do you propose? (The pirates are all extremely logical and greedy, and all want to live.)
answer will be disclosed a week later should no one manages to get it correctly.
5 pirates on an island have 100 gold coins to split among themselves. They divide the loot as follows: The senior pirate proposes a division and everyone votes on it. Provided at least half the pirates vote for the proposal, they split the coins that way. If not, they kill the senior pirate and start over. The next most senior (surviving) pirate then proposes his own division plan, and they vote by the same rules and either divide the loot or kill the senior pirate, as the case may be. The process continues until one plan is accepted.
Suppose you are the most senior pirate. What division do you propose? (The pirates are all extremely logical and greedy, and all want to live.)
answer will be disclosed a week later should no one manages to get it correctly.
posted by cLeMeNt at 3:17 PM
9 Comments:
hey
i suppose they can split the 100 coins among the first 3 most senior pirates equally. the other 2 gets nothing.
i take back, haha.
first person who try, i very touched..
ur ans is not incorrect, just that if u r the most senior pirate, there's a way u can get more than your distribution of 33.333
need to clarify,
when they vote, isit the remaining pirates (less the most senior) who votes or including the most senior one as well?
for eg, if you meant the latter version, when the grp is left with only 2 people, is it then the most senior one of the two who will surely get the money? because he is one vote liao mah (out of two)
haha, i working on the answer. but need this to substantiate my argument
anyway i m kangli
wah.. kangli, i think u r quite close to the ans.
anyway, as for ur queries, yes, the most senior pirate will always vote.
in the case when there are only 2 pirates, the most senior pirate's own vote will be enough to carry out the division.
Ok, my answer:
Let's call the most senior pirate "5" and the least senior "1"
The gist of it is to distribute the money to 5, 3, 1
5 can take 90% while 3 and 1 take 5% each. (The ratio doesnt really matter. But 5 can definitely take more than 50%)
Because 3 and 1 has to vote for this division no matter what if they think further.
If they do not vote, and 5 is killed, then 4 will take over. 4 will divide the money between himself and 2.
Why?
Because if 2 dun vote for 4's method of division, then 3 will take over as most senior and he can manipulate such that 3 and 1 get the money and 2 get nil. That is why 2 will definitely vote for 4's method of division.
let's say 4 gets killed and 3 takes over. Then, 1 definitely has to vote for 3's method of division because if he dun, then 2 will take over as most senior and 2's vote is enough to get him all the money.
so 1 will definitely not get money unless 3 offers him in the scenario that 3 becomes the most senior. and 3 will definitely not get money unless he becomes the most senior. But both scenarios are unlikely because when 4 is the most senior, he will certainly get 2's vote and 3 will never have the chance to be most senior.
so for safety sake, they have to agree with 5's method to guarantee that they at least have a share of the money, securing 5's method by virtue of 5's, 3's and 1's votes.
Am i correct?????
excellent.. kangli!!
u sure impress many..
just in case the rest still doesn't understand, i have provided another way of explaining. hope it helps
here's the correct ans:
98:0:1:0:1
Situation 1:
suppose there's only 2 pirates instead of 5.
the senior pirate will propose to have 100:0 because his vote will be enough to carry out the proposal.(1 for, 1 against)
Situation 2:
suppose there's 3 pirates.
the senior pirate could not pull off the same trick of 100:0:0. He needs one more vote in order to carry out the proposal.
In this case he should propose 99:0:1. This will win him the least senior pirate's(pirate #1) vote. y? because pirate #1 will be able to see should him vote against this proposal, they will kill off the most senior pirate, hence leaving him and pirate #2 together. Situation 1 will then occur. he will get nothing from it, hence he win be voting for by this proposal of 99:0:1. He gets 1 coin as to zero.
Situation 3:
Suppose there's 4 pirates. the most senior pirate should propose 99:0:1:0. He only needs two votes. Hence same as situation 2.
Situation 4:
Hence, when there's 5 pirates, the most senior pirate should propose 98:0:1:0:1.
The most senior pirate(pirate#5) will need 1 gold coin to buy over the least senior pirate's(pirate#1) vote. y? because pirate #1 will see that if he votes against the proposal of 98:0:1:0:1, they will be killing off pirate #5, Situation 3 will then occur. He will be getting nothing in that case. Hence, he should be satisfy with this 1 gold coin as to none in situation 3.
well.. since this question is solved, stay tuned next week, where i will post yet another challenging problem...
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