Jamie123 Posted October 12, 2016 Report Share Posted October 12, 2016 (edited) Here is a puzzle I saw in a magazine recently. (I've paraphrased it a bit from the original.) **** There was once a handsome young scholar who gave such service to his country that the king asked him to name his reward. Now it happened that the scholar loved the king's beautiful daughter, so there was no doubting what his request would be. "Sire," he said. "I would like to marry the princess." "You've got a nerve!" said the king, genuinely surprised. "But a promise is a promise, so I will give you one chance. Return to the palace at noon tomorrow and you will tested. If you pass the test, you may marry the princess. If you fail you will spend the next six months in the castle dungeon eating bread and gruel, as a warning to any other young upstart who might think of asking for my daughter's hand!" So the next day the scholar returned to the palace and was shown into the king's study. "Here," said the king, indicating a collection of objects on the table, "are two identical stone jars and one hundred coins. All the coins are identical, with the exception that fifty of them are copper and fifty gold. No one, other than by looking at them, could tell the copper coins from the gold coins." "Yes, sire" said the scholar, wondering what was coming next. "What I want you to do," continued the king, "Is put all the coins into the jars. You may put as many of each kind of coin into whichever jar you choose, but every coin must go into one or other of the jars. When you have finished, my daughter will come into the room blindfolded, and take one coin from one jar. If she chooses a gold coin you may marry her, but if she chooses a copper one it's off to the dungeon with you!" Question: how many of each coin should the scholar put into each jar? **** (I'm pretty sure I know what the optimal solution is... though I'm mindful of the cautionary tale of Monty Hall!) Edited October 12, 2016 by Jamie123 Quote Link to comment Share on other sites More sharing options...
Guest Posted October 12, 2016 Report Share Posted October 12, 2016 (edited) I'd put all the copper ones in the bottoms of the jars, then place all the gold coins on top. If I knew that the princess loved me in return, I'd place them with copper at the bottom and gold at the top of one jar and one lone gold coin in the second jar - no coppers. Edited October 12, 2016 by Guest Quote Link to comment Share on other sites More sharing options...
CV75 Posted October 12, 2016 Report Share Posted October 12, 2016 1 hour ago, Jamie123 said: Here is a puzzle I saw in a magazine recently. (I've paraphrased it a bit from the original.) **** There was once a handsome young scholar who gave such service to his country that the king asked him to name his reward. Now it happened that the scholar loved the king's beautiful daughter, so there was no doubting what his request would be. "Sire," he said. "I would like to marry the princess." "You've got a nerve!" said the king, genuinely surprised. "But a promise is a promise, so I will give you one chance. Return to the palace at noon tomorrow and you will tested. If you pass the test, you may marry the princess. If you fail you will spend the next six months in the castle dungeon eating bread and gruel, as a warning to any other young upstart who might think of asking for my daughter's hand!" So the next day the scholar returned to the palace and was shown into the king's study. "Here," said the king, indicating a collection of objects on the table, "are two identical stone jars and one hundred coins. All the coins are identical, with the exception that fifty of them are copper and fifty gold. No one, other than by looking at them, could tell the copper coins from the gold coins." "Yes, sire" said the scholar, wondering what was coming next. "What I want you to do," continued the king, "Is put all the coins into the jars. You may put as many of each kind of coin into whichever jar you choose, but every coin must go into one or other of the jars. When you have finished, my daughter will come into the room blindfolded, and take one coin from one jar. If she chooses a gold coin you may marry her, but if she chooses a copper one it's off to the dungeon with you!" Question: how many of each coin should the scholar put into each jar? **** (I'm pretty sure I know what the optimal solution is... though I'm mindful of the cautionary tale of Monty Hall!) None -- the king lied and broke his promise, telling the scholar to name his reward, knowing that he would place a subsequent condition on granting it. Jamie123 1 Quote Link to comment Share on other sites More sharing options...
unixknight Posted October 12, 2016 Report Share Posted October 12, 2016 (edited) 6 hours ago, Carborendum said: I'd put all the copper ones in the bottoms of the jars, then place all the gold coins on top. If I knew that the princess loved me in return, I'd place them with copper at the bottom and gold at the top of one jar and one lone gold coin in the second jar - no coppers. It doesn't say whether she can examine the jars before plucking a coin... so I'm assuming once she picks a jar that's the one she has to draw from. It also doesn't say whether she has to pluck one from the top or whether it's assumed the coin will be drawn at random from the chosen jar. I'm not a probability expert, but my quick and dirty calculation tells me that this is probably optimal. It means you have the best possible chance of winning here. If she chooses the jar with just the gold coin, you win outright. There's a 50% chance this will occur, if she has to start by picking a jar without checking it first. If she chooses the jar with 99 coins in it, and takes one from the top, you win, if the puzzle allows her to choose specifically from the top. If she chooses the jar with 99 coins but picks one at random, you have slightly less than a 50% chance that she will pull a gold coin. I don't know how to calculate the overall probability of success, but it seems to me that this approach is the best way to maximize your odds, assuming everything else is random. Edited October 12, 2016 by unixknight Jamie123 1 Quote Link to comment Share on other sites More sharing options...
bytebear Posted October 12, 2016 Report Share Posted October 12, 2016 (edited) one gold coin in jar A, and 49 gold coins and 50 copper coins in jar B. You have roughly a 2/3 chance of winning. If she picks jar A, you win outright. If she pics jar B, and a gold coin (49/99 chance) you win. If she pics Jar B, and a copper coin (50,99) you lose. Edited October 12, 2016 by bytebear Jamie123 1 Quote Link to comment Share on other sites More sharing options...
NightSG Posted October 12, 2016 Report Share Posted October 12, 2016 Put all the copper coins in one jar, all the gold in the other, and pitch the copper filled one out the window. Sunday21, Backroads and Jamie123 3 Quote Link to comment Share on other sites More sharing options...
Jamie123 Posted October 19, 2016 Author Report Share Posted October 19, 2016 On 12/10/2016 at 5:41 PM, CV75 said: None -- the king lied and broke his promise, telling the scholar to name his reward, knowing that he would place a subsequent condition on granting it. Quite right - this was me misquoting the problem a bit. I believe in the original he asked the king for a "chance" to marry her. My bad. On 12/10/2016 at 11:25 PM, bytebear said: one gold coin in jar A, and 49 gold coins and 50 copper coins in jar B. You have roughly a 2/3 chance of winning. If she picks jar A, you win outright. If she pics jar B, and a gold coin (49/99 chance) you win. If she pics Jar B, and a copper coin (50,99) you lose. Yes, this was my solution. I cannot imagine any way of improving the odds any further. (Other than sneaky putting the gold on top or pitching jars through windows; the sort of thing James T. Kirk got commended for when he was at Starfleet Academy ;).) unixknight and bytebear 2 Quote Link to comment Share on other sites More sharing options...
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