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Nir Dahan Inner circle Munich, Germany 1390 Posts |
This one you guys probably seen before (it was in one of MG books) but just in case you didn't...
since Tomas destroyed one of my last puzzles (and rightfully so) he will get to be the evil guy in this puzzle. so Stan and Tomas play a game on a turnable square table. - the square table has 4 switches (one in each corner). - the switches are 'press switches' - with each push they change their state. Their on/off condition is unknown and can not be detected from touch alone - Stan can press simultaneously one, two, three or all four of the switches - if ALL are in the ON state in the end of a turn - a bell will ring and Stan will win the game - Tomas is a bit nasty - he sets the switches to 'some' state before Stan arrives to play the game - Tomas is actually mean, since he blindfolds Stan for this game - Tomas is absolutely evil since after each move by Stan (pressing 1,2,3 or 4 switches) he turns the table 0, 90, 10 or 270 degrees, without the possibility for Stan to realize the amount of turning. Stan is as we all know clever - can Stan find a strategy for the bell to ring in a finite amount of steps? Tomas is also darn clever, can he prevent Stan from winning if Stan has to declare ALL his moves in advance? (this way Tomas could react by turning the table in a different manner for each move Stan is about to do) enjoy, N |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
I meant the turning is 0, 90 180, or 270 degrees
if this is too easy for you try with 8 switches... |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Another point...
the solution should be in a minimum number of steps or prove this doesn't exist. obviously changing in random will solve this EVENTUALLY. but, if Stan has to declare ALL moves in ADVANCE, Tomas could arrange that with a pure random order he will never let Stan win. Or could he? |
stanalger Special user St. Louis, MO 998 Posts |
Haven't given this enough thought to convince myself that this is a minimum, but I have a 16-step solution. (I assume the bell is not enabled until AFTER Stan makes a move. If the bell is also enabled BEFORE Stan makes a move, then I can trim it down to a 15-step solution.)
Has anyone come up with anything shorter? |
TomasB Inner circle Sweden 1144 Posts |
This tells me that even if Stan announced all his moves in advance Tomas would not be able to counteract it.
I'd think it'd be reasonable to assume that the bell rings as soon as all buttons are in "on" so the starting case where all buttons are in "on" can be ignored. At least that's how I'd build the board. /Tomas |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
As usual ...
Stan gets it right. 15 steps is the minimum (That I know of...) and just for fun, some references: http://www.ms.uky.edu/~jrge/Papers/BBP.pdf http://www.jstor.org/pss/2690109?cookieSet=1 the Martin Gardner reference is at the end of the first link |
stanalger Special user St. Louis, MO 998 Posts |
Didn't mean to kill interest in this one. OK, we know a 15 step solution exists.
Can you find one? Stan |
Bill Palmer Eternal Order Only Jonathan Townsend has more than 24312 Posts |
I have a one step solution, which is based upon a principle that is discussed in a book by Parrish and Weigle called Do that Again. The principle in question is on page 17 of the book and is called "The 'Direct' Divination."
I will not post it. I will reveal this to one person only. That person will, of necessity, not be anyone who has posted in this thread.
"The Swatter"
Founder of CODBAMMC My Chickasaw name is "Throws Money at Cups." www.cupsandballsmuseum.com |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Bill,
allow me to doubt your solution... |
The Magic Cafe Forum Index » » Puzzle me this... » » Tomas and Stan in a battle of minds (0 Likes) |
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