TADM2E 2.52 - Revision history

Matt: Undo revision 795 by EthanGamer (talk)

2020-07-23T13:36:15Z

Undo revision 795 by EthanGamer (talk)

EthanGamer: Replaced content with "This"

2020-07-14T01:59:23Z

Replaced content with "This"

Fan cowboys 22: Corrected part b.

2017-05-24T01:41:31Z

Corrected part b.

Fan cowboys 22: Correct the answer for situation "b".

2017-05-21T20:59:58Z

Correct the answer for situation "b".

Fan cowboys 22: Formatting again

2017-05-21T20:03:16Z

Formatting again

Fan cowboys 22: Bullet points instead of programming font.

2017-05-21T20:01:21Z

Bullet points instead of programming font.

Fan cowboys 22: Replace parentheses

2017-05-21T19:59:29Z

Replace parentheses

Fan cowboys 22: Grammar errors and further explanation.

2017-05-21T19:57:14Z

Grammar errors and further explanation.

Fan cowboys 22: Grammar errors as well correcting the 6-pirate situation in option "a".

2017-05-21T19:53:03Z

Grammar errors as well correcting the 6-pirate situation in option "a".

Nishant at 12:45, 25 May 2015

2015-05-25T12:45:46Z

← Older revision		Revision as of 13:36, 23 July 2020
Line 1:		Line 1:
−	This	+	This problem is a famous game-theoretical scenario called the pirate game (http://en.wikipedia.org/wiki/Pirate_game). Assume the senior pirate gets to vote.
		+
		+	Where there is only 1 indivisible dollar:
		+	2 pirates - The senior pirate gets it.
		+	3+ pirates - The least senior pirate gets it.
		+
		+	In general, every 2 + 2^K (k >= 1) pirate will survive, while the others will die
		+
		+	'''Another Answer''' :
		+	Assume senior pirate also gets to vote.
		+
		+	Based on pirates inherent tendency -
		+
		+	'''a.''' They want to kill other pirates even if it does not affect their outcome -
		+
		+	2 pirates: Senior gets it.
		+
		+	3 pirates: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.
		+
		+	4 pirates: 2nd or 3rd-least-senior pirate will get gold (equally likely) because 1st will vote for kill irrespective of whether he/she gets the gold or not, and the 2nd or 3rd-least-senior pirate will vote for the plan if he/she
		+	gets the gold respectively.
		+
		+	5 pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.
		+
		+	6 pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below—recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone vs. a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
		+
		+	• 4th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.
		+
		+	• 3rd-least-senior pirate: would agree to receive the coin since there would only be a 50% chance he/she would get it as described in the eventually inevitable "4 pirates" situation.
		+
		+	• 2nd-least-senior pirate: same reasoning as above.
		+
		+	• Least senior pirate: the least senior pirate would agree to receive the coin since he/she would have a 0% chance to receive the gold as described in the eventually inevitable "4 pirates" situation.
		+
		+	Thus the result would be that no one dies and either the first, second, third, or fourth-least-senior pirate would receive the coin.
		+
		+	'''b.''' They want as many other pirates to live if it doesn't affect their outcome -
		+
		+	Senior most pirate gets the gold.

← Older revision		Revision as of 01:59, 14 July 2020
Line 1:		Line 1:
−	This ~~problem is a famous game-theoretical scenario called the pirate game (http://en.wikipedia.org/wiki/Pirate_game). Assume the senior pirate gets to vote.~~	+	This
−
−	~~Where there is only 1 indivisible dollar:~~
−	~~2 pirates - The senior pirate gets it.~~
−	~~3+ pirates - The least senior pirate gets it.~~
−
−	~~In general, every 2 + 2^K (k >= 1) pirate will survive, while the others will die~~
−
−	~~'''Another Answer''' :~~
−	~~Assume senior pirate also gets to vote.~~
−
−	~~Based on pirates inherent tendency -~~
−
−	~~'''a.''' They want to kill other pirates even if it does not affect their outcome -~~
−
−	~~2 pirates: Senior gets it.~~
−
−	~~3 pirates: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.~~
−
−	4 pirates: 2nd or 3rd-least-senior pirate will get gold (equally likely) because 1st will vote for kill irrespective of whether he/she gets the gold or not, and the 2nd or 3rd-least-senior pirate will vote for the plan if he/she
−	~~gets the gold respectively.~~
−
−	5 pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.
−
−	6 pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below—recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone vs. a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
−
−	• 4th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.
−
−	~~• 3rd-least-senior pirate: would agree to receive the coin since there would only be a 50% chance he/she would get it as described in the eventually inevitable "4 pirates" situation.~~
−
−	~~• 2nd-least-senior pirate: same reasoning as above.~~
−
−	• Least senior pirate: the least senior pirate would agree to receive the coin since he/she would have a 0% chance to receive the gold as described in the eventually inevitable "4 pirates" situation.
−
−	~~Thus the result would be that no one dies and either the first, second, third, or fourth-least-senior pirate would receive the coin.~~
−
−	~~'''b.''' They want as many other pirates to live if it doesn't affect their outcome -~~
−
−	~~Senior most pirate gets the gold.~~

← Older revision		Revision as of 01:41, 24 May 2017
Line 37:		Line 37:
	'''b.''' They want as many other pirates to live if it doesn't affect their outcome -		'''b.''' They want as many other pirates to live if it doesn't affect their outcome -

−	~~2 pirates:~~ Senior ~~gets it~~	+	Senior most pirate gets the gold.
−
−	3 pirates: Since a pirate will always vote along with another pirate's plan if he/she gets the gold (since you get the gold and want to maximize the number of pirates who live), the most senior pirate would give the gold to any of the remaining two pirates.
−
−	~~4 pirates: The same argument above is applicable here; thus the most senior pirate gives the gold to any of the other three pirates.~~
−
−	5 pirates: There will be at least 3 pirates (more than half) that don't receive the gold; and since each one would have greater than 0% chance of receiving the gold if the 2nd-most-senior pirate gets to decide (as described above), they would all vote to kill the senior most pirate. From here it becomes the "4 pirates" situation where one of the three least senior pirates will receive the gold.
−
−	6 pirates: The 2nd-most-senior pirate knows he/she is dead if he/she has to pick the pirate to receive the gold; thus he/she will always vote in favor for the most senior pirate's plan. To receive the last vote necessary to live, the senior most pirate ~~can then decide to give it to any of the other 4 pirates (since that pirate will get the gold and maximize the number of pirates who live). Thus all pirates live and one of the 4 least senior pirates~~ gets the gold.

@@ Line 35: / Line 35: @@
 Thus the result would be that no one dies and either the first, second, third, or fourth-least-senior pirate would receive the coin.
-'''b.''' They want other pirate to live if it doesn't affect their outcome -
+'''b.''' They want as many other pirates to live if it doesn't affect their outcome -
-Senior most pirate always gets the coin.
+pirates: Senior gets it

@@ Line 25: / Line 25: @@
 pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below—recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone vs. a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
- • 4th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.
+• 4th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.
-Thus the result would be that no one dies and either the first, second, third, or fourth least senior pirate would receive the coin.
+• 3rd-least-senior pirate: would agree to receive the coin since there would only be a 50% chance he/she would get it as described in the eventually inevitable "4 pirates" situation.
 '''b.''' They want other pirate to live if it doesn't affect their outcome -
 Senior most pirate always gets the coin.

@@ Line 23: / Line 23: @@
 pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.
-pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below (recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone or has a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
+pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below—recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone vs. a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
 th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.

@@ Line 16: / Line 16: @@
 pirates:  Senior gets it.
-pirate: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.
+pirates: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.
 pirates: 2nd or 3rd-least-senior pirate will get gold (equally likely) because 1st will vote for kill irrespective of whether he/she gets the gold or not, and the 2nd or 3rd-least-senior pirate will vote for the plan if he/she
@@ Line 23: / Line 23: @@
 pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.
-pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the coin any of the remaining four pirates. The reason for each is below:
+pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below (recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone or has a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
 th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.

@@ Line 14: / Line 14: @@
 '''a.''' They want to kill other pirates even if it does not affect their outcome -
-pirates - Senior gets it.
+pirates:  Senior gets it.
-pirates - Smallest gets it, because 2nd pirate will vote for kill. So, in order to live he must give dollar to smallest.
+pirate: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.
-pirates - 2nd or 3rd smallest will get with 50% chances, because 1st will vote for kill irrespective of weather he gets the dollar or not. And 2nd or 3rd will vote for 4th if they
+pirates: 2nd or 3rd-least-senior pirate will get gold (equally likely) because 1st will vote for kill irrespective of whether he/she gets the gold or not, and the 2nd or 3rd-least-senior pirate will vote for the plan if he/she
-get the dollar.
+gets the gold respectively.
-pirates - He is certainly going to die, irrespective of his proposal. Whosoever he chooses other three/four will vote against him.
+pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.
-pirates - Here 5th will vote for 6th irrespective of weather he gets the dollar, otherwise he is going to die. And 1st will vote for 6th if he gets the dollar, because if he doesn't he doesn't get the dollar(because the case will reduce to 4 pirates).thus, 6th will live and 1st will get the coin.
+pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the coin any of the remaining four pirates. The reason for each is below:
 '''b.''' They want other pirate to live if it doesn't affect their outcome -
 Senior most pirate always gets the coin.

← Older revision		Revision as of 12:45, 25 May 2015
Line 6:		Line 6:

	In general, every 2 + 2^K (k >= 1) pirate will survive, while the others will die		In general, every 2 + 2^K (k >= 1) pirate will survive, while the others will die
		+
		+	'''Another Answer''' :
		+	Assume senior pirate also gets to vote.
		+
		+	Based on pirates inherent tendency -
		+
		+	'''a.''' They want to kill other pirates even if it does not affect their outcome -
		+
		+	2 pirates - Senior gets it.
		+
		+	3 pirates - Smallest gets it, because 2nd pirate will vote for kill. So, in order to live he must give dollar to smallest.
		+
		+	4 pirates - 2nd or 3rd smallest will get with 50% chances, because 1st will vote for kill irrespective of weather he gets the dollar or not. And 2nd or 3rd will vote for 4th if they
		+	get the dollar.
		+
		+	5 pirates - He is certainly going to die, irrespective of his proposal. Whosoever he chooses other three/four will vote against him.
		+
		+	6 pirates - Here 5th will vote for 6th irrespective of weather he gets the dollar, otherwise he is going to die. And 1st will vote for 6th if he gets the dollar, because if he doesn't he doesn't get the dollar(because the case will reduce to 4 pirates).thus, 6th will live and 1st will get the coin.
		+
		+	'''b.''' They want other pirate to live if it doesn't affect their outcome -
		+
		+	Senior most pirate always gets the coin.