2021/7/26. The “more” or “more than or equal to”
I met one difficult problem.
The original story(English) is below site’s problem.
And changed story(Japanese) includes changed rule.
I think that this change is from mistranslation.
But this change causes the problem MORE difficult.
The original story
http://www.bigriddles.com/riddle/ten-pirates-and-their-gold
[The problem part]
Each pirate will vote against a proposal if they know that they would end up with more gold if that proposal were to fail.
[Changed rule]
Each pirate will vote against a proposal if they know that they would end up with “more or equal to” gold if that proposal were to fail.
It is a miracle difficult problem caused by mistranslation.
“より大きい” corresponds to "more than".
“以上” corresponds to "more than or equal to".
“未満” corresponds to "less than".
“以下” corresponds to "less than or equal to".
In addition to the model answer, there are the following answers.
Model answer
[4 people]
A: B: C: D (boss) = 0: 1: 0: 99
[5 people]
A: B: C: D: E (boss) = 1: 0: 1: 0: 98
[6 people]
A: B: C: D: E: F (boss) = 0: 1: 0: 1: 0: 98
[7 people]
A: B: C: D: E: F: G (boss) = 1: 0: 1: 0: 1: 0: 97
[8 people]
A: B: C: D: E: F: G: H (boss) = 0: 1: 0: 1: 0: 1: 0: 97
[9 people]
A: B: C: D: E: F: G: H: I (boss) = 1: 0: 1: 0: 1: 0: 1: 0: 96
[10 people]
A: B: C: D: E: F: G: H: I: J (boss) = 0: 1: 0: 1: 0: 1: 0: 1: 0: 96
Answer 1: A pattern in which the allocation is determined by four people
[4 people]
A: B: C: D (boss) = 2: 0: 0: 98
[5 people]
A: B: C: D: E (boss) = 0: 1: 1: 0: 98
[6 people]
A: B: C: D: E: F (boss) = 1: 0: 0: 1: 0: 98
[7 people]
A: B: C: D: E: F: G (boss) = 0: 1: 1: 0: 1: 0: 97
[8 people]
A: B: C: D: E: F: G: H (boss) = 1: 0: 0: 1: 0: 1: 0: 97
[9 people]
A: B: C: D: E: F: G: H: I (boss) = 0: 1: 1: 0: 1: 0: 1: 0: 96
[10 people]
A: B: C: D: E: F: G: H: I: J (boss) = 1: 0: 0: 1: 0: 1: 0: 1: 0: 96
Answer 1 does not exist in the original story.
In the original story, only when you can get "more" gold coins, you oppose it, so it will be "A=1 coin when 3 people" and "A=1 coin when 4 people". (0 gold coins are unconditionally opposed.)
In this problem, when you get "more than or equal to" gold coins, you are against it, so if you have "A=1 coin when 3 people", you can choose "A=2 coins when 4 people".
And if the distribution for 5 people is answer 1, the distribution for 4 people is answer 1.
The reason why D chooses this allocation when there are four people in answer 1 is because life> gold coins.
Then, due to the existence of answer 1, if J chooses the model answer, I chooses answer 1 and J is executed.
Also, if J chooses answer 1, I chooses the model answer and J is executed.
J knows that if he decides to take 96 coins, he will be executed, so the distribution of A-J's game theory, which is infinitely clever, begins.
(I wrote this blog with google translation. Some mistranslation may be included.)