Pennies on a Table

You pass away and, though you have not been a particularly bad person in life, you have not been a particularly good one either. Waiting in the reception room of hell, the devil comes out to meet you. “Well,” says the devil, “Since you have not been that bad, I am going to give you a chance to get out of here.” The two of you then enter another room off to the side of the reception. In the middle of the room is a giant circular table and next to the walls are many sacks of coins. The devil continues, “We are going to play a game. We will take turns putting coins down flat on the table. I will put down a coin and then you will put down a coin, and so on. The coins cannot overlap and they cannot hang over the edge of the table. The last person to put down a coin wins, or equivalently, the last person who can no longer put a coin down on the table loses. Since you have never played this game before, I will also let you decide if you want to play first.” Can you think of a winning strategy for the game?

Problem (and phrasing) communicated by Justin Bledin.

39 Comments

  1. Steven Miller on September 30, 2015 at 7:38 pm

    OK, but going first ensures you win….



  2. Lucas on September 30, 2015 at 7:05 pm

    I do not want to play first or second, I don’t want to play at all.



  3. Steven Miller on July 25, 2013 at 2:44 am

    there’s a soln that’s easy to state //s (email me at [email protected])



  4. abcd on July 24, 2013 at 11:15 pm

    I have a solution but you would need a ruler to measure distances exactly…



  5. Steven Miller on September 22, 2012 at 3:51 pm

    dean: correct — email me at sjm1 AT williams.edu



  6. Daan on September 21, 2012 at 11:06 pm

    You go first and put a coin in the center.
    After that, you mirror every move he makes through your first coin.
    This way, the table will end up perfectly symmetrical and you have the last move.



  7. Steven Miller on June 6, 2012 at 4:22 am

    You can do it with them flat. /s



  8. Anonymous on June 5, 2012 at 9:17 pm

    obvious. put the coins on their sides. it doesnt say that they have to be flat on the table



  9. Steven Miller on April 2, 2012 at 1:41 pm

    I’ll send a hint first. //s



  10. jo on April 2, 2012 at 12:00 pm

    can u email me the answer pls?
    [email protected]



  11. Steven Miller on March 29, 2012 at 8:20 pm

    monkey68pl: well done, not posting as it’s the soln



  12. monkey68pl on March 29, 2012 at 7:49 pm

    Play [[deleted]] I hope that you can understand my english – I know it’s not very good.

    Great riddle, anyway:]



  13. Steven Miller on March 8, 2012 at 2:05 am

    To Anonymous
    98.251.65.153
    Submitted on 2012/03/08 at 12:06 am: correct, well done! not posting as it’s the soln. //s



  14. Steven Miller on February 26, 2012 at 6:02 am

    both bags have the same number of coins //s



  15. Stan on February 26, 2012 at 4:48 am

    Can I choose more than one bag of coins?
    If not then just pick a bigger bag of coins so you know you’ll have more than the devil so you can play more



  16. Steven Miller on February 18, 2012 at 9:51 pm

    To anonymous; correct (not posting as it’s the soln)



  17. Steven Miller on February 18, 2012 at 2:03 am

    not quite — what if the devil goes in the middle earlier?



  18. Anonymous on February 17, 2012 at 10:00 pm

    wait until theres room for only like three or four coins and put down one in the middle, since they cannot overlap he should not be able to put another one down.



  19. Steven Miller on January 30, 2012 at 3:51 am

    you can’t move coins, but there is a way to win if you go first



  20. kevin K on January 30, 2012 at 12:16 am

    can i move the other coins? if so then i should go first. if not then i’m screwed since the devil has had all of eternity to practice this retarted game.



  21. Steven Miller on January 22, 2012 at 3:00 pm

    You’re on teh right track, but not there yet — email me at [email protected] if you want to discuss more.



  22. Inquisitive in Ohio on January 22, 2012 at 5:31 am

    Circles of coins tend to be made of odd numbers. If the circular table is to be filled without gaps then the person who placed the first coin would always win. (is the devil allowed to place a coin so that it would screw up my logic?)



  23. Steven Miller on January 18, 2012 at 7:44 pm

    The devil is being very kind and giving you a chance to play a game of skill and not luck — take him/her up on the offer!



  24. Joseph on January 18, 2012 at 7:33 pm

    Can’t we just play battleship like in Bill and Ted’s Bogus Journey?



  25. Steven Miller on January 16, 2012 at 2:42 am

    there are more than enough coins to cover the table 1000 times over. email me ([email protected]) if you want another hint. /s/



  26. Anonymous on January 15, 2012 at 3:42 pm

    if there are less coins than the whole table then just let the devil play first, right? if there are more… isn’t it impossible to say, since it relies on fact who starts? i guess not, cause it has a solution, i just cant think of one.



  27. Steven Miller on December 22, 2011 at 9:53 pm

    Ross: correct, well done! Not posting as it’s the soln.



  28. Steven Miller on November 24, 2011 at 1:45 am

    Bryan: correct! not posting as it’s the soln



  29. Steven Miller on November 10, 2011 at 8:26 pm

    Can you send a few more details to [email protected] — the table doesn’t have to be entirely filled, as there can be gaps. You might have the soln, just have to be careful how you phrase it.



  30. Milind on November 10, 2011 at 8:53 am

    The table will be fully filled by ‘odd’ number of coins.
    Hence winning strategy is to play first



  31. Steven Miller on November 7, 2011 at 8:03 pm

    Whomever just posted: Submitted on 2011/11/07 at 8:00 pm: correct!



  32. Steven Miller on November 7, 2011 at 1:47 am

    You can do this without being so violent….



  33. Tommy Le on November 6, 2011 at 6:33 pm

    easy. in the end, if u cant put the coin just put the coin and push others off the table.



  34. Steven Miller on September 12, 2011 at 2:17 am

    No and no.



  35. Shane on September 11, 2011 at 5:35 pm

    is each coin put down after the 1st required to touch the first? Is each coin required to be touching a coin preceding it? I think I have the answer but only if these 2 assumptions are true.



  36. Steven Miller on September 2, 2011 at 6:01 pm

    You don’t need to count the number of coins. You know their sizes and you can see the whole table. What is the winning strategy?



  37. Thanh Cong on September 2, 2011 at 4:48 pm

    Can the guy count the number of coins before he choose?
    Since you said the table is giant, I assume that it is possible to put all coins on the table. In this case, if the number of coins is odd then the guy should start first, otherwise he should let the devil start first.



  38. Jordan Ladd on April 14, 2011 at 9:05 pm

    You pick first. The devil will always start a new ring from a coin placed in the exact center.



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