ah! cool. it strikes me that another way to find this is to look for rooms that are two rooms away from the same value. eg there are four rooms each with a value zero two rooms away from 5. another way to see these is to fold the floorplan and see if any numerals overlap. you can fold twice into quarters with 5 at the center of the pivoting and zeros all fall onto each other. what I think would be interesting is to explore the corners a bit more. what's really going on? would be interesting to explore this wrapped into a ball so the edges hit and zeros are next to each other. and how does the problem change if there are 12 numbered rooms instead of 9 in the middle? and what if a hexagon or triangle etc is used? On Mon, Oct 25, 2010 at 10:26 AM, <mbgreen@cis.upenn.edu> wrote:
There are only 4 corners, and 1 orientation in each corner that is ambiguous if you ask for two directions at right angles to each other. If you ask for "front/back" then 2, 4, 6, 8 are ambiguous if you are facing outwards, and 1, 7 if you are facing up, down respectively, 1, 3 ambiguous if facing left, right, 3, 9 if facing up, down, and 7, 9 if facing left, right. So I think the right angle query is the better of the 2 alternatives you propose, and the probability of success is 8/9 (4 failures out of 36 possibilities). I haven't thought about it for logner than it took to jot down this response, so I don't want to claim that this is optimal (although by symmetry of potential failures, my hunch is that this is optimal). ----- Message from gantonick@post.harvard.edu --------- Date: Mon, 25 Oct 2010 10:15:29 -0700 From: Gary Antonick <gantonick@post.harvard.edu> Reply-To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] What is my cell-number To: math-fun <math-fun@mailman.xmission.com>
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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