am curious so I'll take an initial stab and see if someone else solves. at first seems 100%. am not sure because I don't quite get the concept. two insights so far: 1) grid is symmetrical, so question pairs simplify to either front/right or front/back. 2) front/right doesn't work because of corners (edges are all zeros) So you ask what's in front and what's behind you. am guessing there's a cool way to show this. for example, you're facing one of four rooms, so you could unravel the matrix and present as four different room by room grids and plot the points to see each front/back combination is unique. hard to see as currently presented in matrix form. On Mon, Oct 25, 2010 at 8:51 AM, Eric Angelini <Eric.Angelini@kntv.be>wrote:
Hello Math-Fun,
... slightly adapted from a puzzle found here (might
be old hat): "This Book Does Not Exist: Adventures In
The Paradoxical", by Gary Hayden and Michael Picard;
+---+---+---+---+---+
| 0 | 0 | 0 | 0 | 0 |
+---+---+---+---+---+
| 0 | 1 | 2 | 3 | 0 |
+---+---+---+---+---+
| 0 | 4 | 5 | 6 | 0 |
+---+---+---+---+---+
| 0 | 7 | 8 | 9 | 0 |
+---+---+---+---+---+
| 0 | 0 | 0 | 0 | 0 |
+---+---+---+---+---+
You wake up tighten on a chair in one of the cubic
cells with number 1 to 9 -- but in which one?
You are surrounded by four similar walls -- you don't
know which one you are facing: for instance, should
you be in cell #4, wouldn't you know if you are facing
the wall between your cell and the cell #7, or #5,
or #1 or #0.
You may ask two questions to the warden -- one after
the other; he will give you the correct answers, one
after the other.
The questions you may ask are only those:
- What cell number has the cell in front of me?
- What cell number has the cell on my right?
- What cell number has the cell behind me?
- What cell number has the cell on my left?
If you then guess the cell number you are occupying,
you will be free -- if not you'll be killed.
What are my survival odds if I'm a good math-puzzler?
Best,
É.
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