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.
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
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)?
I can do less — email me at [email protected]
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?
I’d say it’s 90 degrees, turning one-quarter of a circle
what is a rotation
is it 180 degree or 360 degree or what???
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
email me at sjm1 AT williams.edu
It can be done in seven.
Flip two opposites, two beside each other, two opposites, one, two opposites, two beside each other, two opposites
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)
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
I think that’s reasonable.
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…
no (sjm1 AT williams.edu)
is it allowed to take some coins before rotating the square?
John: email me at sjm1 AT williams.edu to discuss your soln
sure, sent
This riddle is driving me crazy. Can I get a hint?
that can vary
Is the square always rotated the same number of turns–or does that vary?
no, there is an answer — email sjm1 AT williams.edu for a hint….
there’s no definite answer.. this all depends on luck… i can move the square and make u unturn what u have turned..
Well done — if you email me at sjm1 AT williams.edu we can exchange answers.
ive got 7 moves, assuming you dont know wether they are allready all heads or all taills up to begin with
I don’t know how to do it in 6 — can you send your soln to sjm1 AT williams.edu?
it takes at most 6 requests to identify if I have got the coins. Fewer if I am lucky.
almost
8
Sorry, a bit too high. Email me at sjm1 AT williams.edu to chat more. //s
16
but you can’t stack as they have to be in the corners….
24 Moves. Stack the quarters, then there will be 24 different ways to arrange them.
Correct, but only if you can SEE the position. The challenge is that the riddle states you’re blindfolded….
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
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).
Would the answer be 13 tries?
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I like this approach, but are you allowed to move a coin to the middle? Good thinking outside the box.
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.