Don’t Flip Out, Square!

A square has a quarter in each corner. You are blindfolded and must get all quarters to be heads up or all to be tails up. You will be told when you have done this. You may flip however many you want, then ask if you are done (this constitutes a turn). The square is then rotated/spun an undisclosed number of times. You then get another turn and so on…

Is there a strategy that is guaranteed to work in a finite number of moves, and if so, what is that smallest number of moves you need to be 100% you’ll be able to have all heads up or all tails up?

Communicated by Jeff Miller.

39 Comments

  1. Steven Miller on February 8, 2021 at 3:46 pm

    on a turn you chose some coins to flip, and you flip those and nothing
    else

    that’s a turn

    you can flip 1, 2 or 3 coins; makes no snese to flip 0 or 4



  2. PG on February 8, 2021 at 3:22 pm

    Am I allow to flip same coin twice in one turn? And am I allow to flip it one by one (but count everytimes I flip)?



  3. Steven Miller on July 28, 2015 at 4:07 am

    I can do less — email me at [email protected]



  4. Chatura111 on July 24, 2015 at 9:39 pm

    I think i got the answer but hard to type it all. I can confirm all the combinations with 9 turns if i followed a certain routine!! is 9 the answer?



  5. Steven Miller on February 18, 2013 at 2:01 am

    I’d say it’s 90 degrees, turning one-quarter of a circle



  6. shashank on February 16, 2013 at 4:44 pm

    what is a rotation
    is it 180 degree or 360 degree or what???



  7. Anonymous on October 30, 2012 at 5:35 am

    you keep saying 7 but i keep getting 8. You start by asking if its already done. thats 1. Then you do 7 rounds of actual flipping. Can i cut it down to 7 questions



  8. Steven Miller on September 7, 2012 at 12:58 am

    email me at sjm1 AT williams.edu



  9. Daan on September 6, 2012 at 11:56 pm

    It can be done in seven.
    Flip two opposites, two beside each other, two opposites, one, two opposites, two beside each other, two opposites



  10. Steven Miller on September 4, 2012 at 1:00 pm

    Sadly, you succumbed to the dark side of the force, and Obi Wan Kenobi cut off your hands and feet. (sjm1 AT williams.edu to discuss more)



  11. Reginald Mosley on September 4, 2012 at 4:49 am

    it can be done in one try. all one must do is feel the coin, and they would know if it was heads or tails



  12. Steven Miller on August 24, 2012 at 6:05 am

    I think that’s reasonable.



  13. Anonymous on August 22, 2012 at 3:59 pm

    Is it given that it’s not done in the beginning? If not, then I have to ask if it’s done before any rotations – does it count as a move? If yes, I got 8 moves…



  14. Steven Miller on August 21, 2012 at 6:16 am

    no (sjm1 AT williams.edu)



  15. pao on August 20, 2012 at 1:56 pm

    is it allowed to take some coins before rotating the square?



  16. Steven Miller on August 3, 2012 at 6:06 pm

    John: email me at sjm1 AT williams.edu to discuss your soln



  17. Steven Miller on July 17, 2012 at 3:44 am

    sure, sent



  18. Dave on July 16, 2012 at 3:44 pm

    This riddle is driving me crazy. Can I get a hint?



  19. Steven Miller on July 13, 2012 at 1:22 am

    that can vary



  20. Christopher T on July 12, 2012 at 6:20 pm

    Is the square always rotated the same number of turns–or does that vary?



  21. Steven Miller on May 22, 2012 at 10:56 am

    no, there is an answer — email sjm1 AT williams.edu for a hint….



  22. alex on May 22, 2012 at 6:33 am

    there’s no definite answer.. this all depends on luck… i can move the square and make u unturn what u have turned..



  23. Steven Miller on May 7, 2012 at 3:08 pm

    Well done — if you email me at sjm1 AT williams.edu we can exchange answers.



  24. Monique on May 7, 2012 at 2:55 pm

    ive got 7 moves, assuming you dont know wether they are allready all heads or all taills up to begin with



  25. Steven Miller on March 30, 2012 at 3:24 pm

    I don’t know how to do it in 6 — can you send your soln to sjm1 AT williams.edu?



  26. David on March 30, 2012 at 3:08 pm

    it takes at most 6 requests to identify if I have got the coins. Fewer if I am lucky.



  27. Steven Miller on March 27, 2012 at 6:30 pm

    almost



  28. sauravshakya on March 27, 2012 at 11:25 am

    8



  29. Steven Miller on March 27, 2012 at 3:56 am

    Sorry, a bit too high. Email me at sjm1 AT williams.edu to chat more. //s



  30. sauravshakya on March 27, 2012 at 3:51 am

    16



  31. Steven Miller on March 21, 2012 at 1:42 am

    but you can’t stack as they have to be in the corners….



  32. Aaron S. on March 20, 2012 at 4:43 pm

    24 Moves. Stack the quarters, then there will be 24 different ways to arrange them.



  33. Steven Miller on March 15, 2012 at 7:03 pm

    Correct, but only if you can SEE the position. The challenge is that the riddle states you’re blindfolded….



  34. Anonymous on March 15, 2012 at 7:00 pm

    0 tries if they are already on the same side, one try if three are tails up and one is heads up, and you accurately pick the heads and turn it tails up



  35. Steven Miller on February 29, 2012 at 1:51 am

    It might be possible to do it in 13; I can do it in significantly less (so as not to give away the answer, b/w 5 and 10).



  36. MooMoo on February 28, 2012 at 10:48 pm

    Would the answer be 13 tries?



  37. Ingram Funeral on June 15, 2011 at 5:10 am

    Great post. I was checking continuously this blog and I am impressed! Very useful info specially the last part 🙂 I care for such info much. I was seeking this particular info for a long time. Thank you and best of luck.



  38. Steven Miller on May 18, 2011 at 3:06 pm

    I like this approach, but are you allowed to move a coin to the middle? Good thinking outside the box.



  39. Geoff on May 17, 2011 at 1:31 am

    It can be done in six tries I believe accurately. If you move one of the quarters into the middle of the square (that way you have a reference point when it is turned), then all you have to do is flip each of the three coins in a non repeating order so that all combinations are carried out. Such that the three coins can either be, HHT, HTT, TTH, THH, HHH, TTT.

    Of course you won’t know which is head or tails initially, but if you give them an initial marking, whether it be correct or not, you will eventually match them all heads or all tails, and then the determinate is whether the quarter in the middle is heads or tails.



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