Coins on chess-board puzzle
in [Theory]
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From: Tim Little on 22 Nov 2009 21:18 On 2009-11-23, dgates <dgates(a)somedomain.com> wrote: > I definitely noticed that my system would work better if you're > allowed to leave the board unaltered. And, even under those > conditions, I also need to re-jigger the numbers. Moving up to the next odd size, it is impossible with a board of 5 squares even if you're allowed to leave it unaltered. I suspect the same is true for size 6, but haven't fully analysed it. - Tim
From: alexy on 23 Nov 2009 09:25 Ted Schuerzinger <fedya(a)hughes.spam> wrote: >On Sun, 22 Nov 2009 09:16:51 -0800, dgates wrote: > >> Let's say you were the first prisoner, and I were the second (and, >> while I know that 2^6 is 64, I don't know what "EXOR" means). What >> would you tell me to look for in order to decode your message to me? > >Assume that the squares are numbered in binary from 000000 to 111111. Starting where? There is nothing in the statement of the puzzle that says you can mark the squares. If you want to assume you can mark them, then just mark the magic square! >Then for each of the six places (the units place to the 32s place) look >at the 32 squares that have 1s in that place. If an odd number of those >squares have 1s in their binary representation, then the parity of that >number is 1; if an even number of those squares have 1s, the parity is >0. When the jailer gives you the secret square, turn over the >appropriate coin to change all six parities to the binary representation >of the secret square. -- Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
From: Patricia Shanahan on 23 Nov 2009 10:04 alexy wrote: > Ted Schuerzinger <fedya(a)hughes.spam> wrote: > >> On Sun, 22 Nov 2009 09:16:51 -0800, dgates wrote: >> >>> Let's say you were the first prisoner, and I were the second (and, >>> while I know that 2^6 is 64, I don't know what "EXOR" means). What >>> would you tell me to look for in order to decode your message to me? >> Assume that the squares are numbered in binary from 000000 to 111111. > > Starting where? There is nothing in the statement of the puzzle that > says you can mark the squares. If you want to assume you can mark > them, then just mark the magic square! As a separate part of their planning, the prisoners need to agree on a numbering system, presumably relative to the door through which they enter the test room. Patricia
From: Ray on 23 Nov 2009 13:18 Patricia Shanahan wrote: > As a separate part of their planning, the prisoners need to agree on a > numbering system, presumably relative to the door through which they > enter the test room. And then they are led into the room through different doors and the whole elegant plan falls apart..... ;-) Bear
From: Risto Lankinen on 23 Nov 2009 15:41
On 23 marras, 20:18, Ray <b...(a)sonic.net> wrote: > And then they are led into the room through different doors and > the whole elegant plan falls apart..... ;-) Hmm... I think a numbering exists where this does not matter (meaning that applying the same algorithm from any corner does not make a difference as long as the coins stay in place). In fact, I think 64 squares can accommodate 8 different states (all four corners plus, say, all mirror images). ObPuzzle: How? - Risto - |