What is the solution to _Maze_ by Christopher Manson?

In room 29, a door to room 17 is hidden upside-down to look like a
table.  Notice that the two leftmost candlesticks are not connected to
the stand.  In addition, the two candles for those sticks are casting
shadows back toward the fool, away from the lit candle on the stand.
This is also hinted at in the first room by the two banners on the
ground, nearest the entryway.  They contain the words "Go" & "17."

Using this door it is clear that there is a 16-step path through the Maze:
1 26 30 42 4 29 17 45 23 8 12 39 4 15 37 20 1.

Several of the rooms have unnumbered exits, but the destinations of these
exits can all be deduced. For example, room 36 has four exits, of which only
two are numbered (7 and 16). But four rooms (7, 16, 26, and 45) have exits
marked 36. Therefore the two unmarked exits in room 36 must lead to rooms 26
and 45. By similar logic, the unmarked exit in room 21 must lead to room 1.

Here is the connectivity matrix (asterisks indicate unnumbered exits):
1. 20 21 26 41
2. 12 22 29
3. 9 18 33* 15*
4. 11 15 16 24 29 43 44 39* 42*
5. 20 22 30 43
6. 40 8* 32*
7. 16 33 36
8. 6 12 29 31 23*
9. 3 18 27*
10. 14 34 41 37*
11. 24 40 4* 19* 32* 39*
12. 2 8 21 39
13. 18 25 27
14. 10 24 43
15. 3 30 37 4*
16. 7 36 4* 32*
17. 6 33 45 29*
18. 3 13 9* 44*
19. 11 31 23* 45*
20. 1 5 27 37*
21. 24 31 44 1* 12*
22. 38 43 2* 5* 42*
23. 8 19 28 45
24. 4* 11* 14* 21*
25. 13 34 35 42*
26. 1 30 36 38
27. 9 13 20*
28. 23 32 43 45
29. 2 8 35 40 4* 17**
30. 5 15 34 42 26*
31. 19 21 44 8*
32. 6 11 16 28
33. 3 7 35 17*
34. 10 25 30*
35. 33 25* 29* 41*
36. 7 16 26* 45*
37. 10 15 20 42
38. 22 40 43 26* 41*
39. 4 11 12
40. 6 11 38 29*
41. 1 10 35 38
42. 4 22 25 30 37
43. 22 38 4* 5* 14* 28*
44. 18 21 4* 31*
45. 17 19 23 28 36

Using this matrix, it is possible to find the shortest distance from
rooms 45 and 1.  These are:
1. 3 0
2. 4 3
3. 3 4
4. 3 3
5. 3 2
6. 2 4
7. 2 3
8. 2 3
9. 4 3
10. 4 2
11. 2 3
12. 3 2
13. 5 3
14. 3 3
15. 4 3
16. 2 3
17. 1 4
18. 4 3
19. 1 3
20. 4 1
21. 3 1
22. 3 3
23. 1 4
24. 4 2
25. 4 3
26. 2 1
27. 5 2
28. 1 4
29. 2 3
30. 3 2
31. 2 2
32. 2 4
33. 2 3
34. 4 3
35. 3 2
36. 1 2
37. 5 2
38. 3 2
39. 3 3
40. 3 3
41, 4 1
42. 4 3
43. 2 3
44. 3 2
45. 0 3

Starting from room 1, and going to rooms that are closer to room 45,
we find this unique shortest possible path:
  1 26 36 45

Now, we can simply retrace our steps to find this six step path:
  1 26 36 45 36 26 1

Or if we prefer never to revisit a room, there is this unique shortest
path:
  1 26 36 45 19 31 21 1

It is unclear whether the author intended for the unmarked doors to be an
alternate solution.  Since we have no direct statements from Christopher
Manson on the subject, we can only speculate on his intentions based
upon indirect evidence.  Such speculation is inherently risky.

While Manson went to the trouble of making sure that as many doors
leave a room as enter a room, this fact alone is not conclusive. Did
Manson intend for the unmarked doors to be one directional?  Why state
that there is a sixteen step path, and set up door 17 as the only way
to achieve this path, if unmarked doors could be used?  Did Manson set
up the unmarked doors to reward people for questioning the assumption
that only marked doors can be used?  Such questions cannot be resolved
without further information from the author.

The year after the book was initially published, VENTURA ASSOCIATES, INC. a
fulfillment house retained by the publisher provided the following
additional clues to those who wrote to them requesting a solution.

(quoting)
Each of the additional clues below applies to one word of the riddle
to be found in room #45 of MAZE:

    1.) I'll tip my hat if the two of you can solve this.

    2.) You can get into these two shoes only if you don't go anywhere.

    3.) You will find two names on the table, and they go together like
doughnut and hole.

    4.) You must choose between two pictures.

    5.) There are no two ways you can read this sign.

    6.) You can see that another two pictures demonstrate their own kind
of symmetry.
(end quote)

The various components of room 45, put together properly produce the
following question:

"What house will all live in?"

W + hat = What
shoe + U (horseshoe shaped) = House
Will (common to both names "---- iam shake spear" and "wood row ---- sun")
awl = All (versus nun = none)
elvi = Live (third reading is "vile")
eye + N (sideways Z) = In

On the table, there are a row of up ended logs and a poster with a
shaking spear and a ideographic sun.  These can be interpreted as "wood
row Will's son" or Woodrow Wilson.  A quote attributed to President
Wilson is: "Without God, the world would be a maze without a clue"

Beginning at the first room of the path, a hint can be phrased:

"Like Atlas, you bear it upon your shoulders."

1:  Like is written backwards on the banner hanging near the entryway.
26: salt + A = Atlas
30: From text, "Why 'O' & 'U'?" = You
42: A Bear is the main feature of this room.
4:  The holes and pegs are a form of intelligence test, abbr. I.T.
    alternately, the torches are I's and the gavel is a T
29: up + on = Upon
17: Why + Oh + You + Are = Your
skip room 45
23: Taken from the text is the word "shoulder" to which we add the S from
    room 8.  This is not entirely satisfying, because the next rooms do a
    good job of providing most of the letters, but not in quite the right
    order.
8:  S
12: U D
39: R and on the tire O
4:  "ELL" in maze on wall spells L
15: hat, hare, heart, helmet, house, hero all start with H
37: sphere, bottle, vase, cone, dice all end with E (clued in text)
20: S

The acceptable answers were "The World, Earth, or Globe."

Scott Purdy wrote the earlier version of this answer and thanked
Andrew C. Plotkin for the information provided by the publisher and
Narciso Jaramillo for his assistance in determining the reasons for
several statements.  Chris McManus proposed the 8 room path through the
Maze. John Bailey located the Woodrow Wilson quote.

Web pages at http://www.frontiernet.net/~jmb184/maze/ contain additional
contributions speculating on the identity of the guide or host through the
Maze and additional observations as to hints and clues found in the rooms.

The contest period is long over; I never found out whether there was a
winner.

I did write away to Ventura Associates for the solution.  This is what
they sent me:

  [A string of numbers representing the path. I forget the exact
  values -- you say you found it, anyway.]

  What house will all live in?
  Like Atlas, you bear it upon your shoulders.
  (The World -- Earth -- The Globe)

I assume that the two lines "What...shoulders." is the riddle, and the
three phrases in parentheses [Editor: the original has "paretheses"] are different acceptable solutions.

-- Andrew C. Plotkin (ap1i+@andrew.cmu.edu)

A friend of mine says that riddles told by storytellers long ago were
different from riddles as we know them these days; they often didn't
contain enough information, and were intended more to show off the
cleverness of the storyteller than to be soluble by the listener.  She
suggests that perhaps the author of "Maze" was inspired by that
tradition.  Which may have made "Maze" a particularly good candidate
for a $10,000 contest, if the publisher didn't really want to give the
money away...

-- Narciso Jaramillo (nj@cs.Berkeley.EDU)

Digging around among old books I found my original copy of the Maze by
Christopher Manson.  Two things of interest to those of us who can't
let the problem go.  Toward more facts which support the puzzle and its
solution: I found a letter, no date from an MJB, presumably [Editor:
the original has "presumable"] employed by a Ventura Associates, Sales
Promotion.  The letter starts: Dear Maze Contestant, and continues with
an explanation [Editor: the original has "explaination"] that the Maze
contest [Editor: the original has "context"] has been extended (sic)
"one last time to September 1, 1987".  It then provides these clues:
[Editor: the six clues, already quoted above, are omitted.]  I can
relate these clues to Scot Purdy's solution and they seem to confirm
the solution.

The other thing of interest was in the front of this book.  Titled
"MAZE $10,000 Prize", it outlines three questions and gives typical game
type of information about rules.  It also promises to send a solution
if you send them a self addressed envelope.  (Which is how I came to
receive the above supplementary [Editor: the original has
"supplimentary"] clues.)

My question is: did anyone win the contest?  Did anyone else send for a
solution?

-- John Bailey (jmb184@servtech.com)

[Editor: from mail quoted by John Bailey:]

Do you have any information about the clues that lead the reader along
the path from one room to the next?  Knowing the path is one thing, but
there are supposed to be reasons for choosing the correct doors.

-- Alexander Boroson (boroson@fas.harvard.edu)

No, that's a new set of questions for me.

-- John Bailey

In addition to the hint, Shakespeare's theater was the Globe, and among
the banners in the first room is the Greek symbol for their goddess of
Earth, a circle with a dot in the center.  (actually, the banner has a
square, and that is only a vague memory.  I'm not sure that the symbol
is correct at all.)

Although a letter has been sent to the publisher, nothing but the
riddle, hint and answer is certain.  In, it, and shoulders are
particularly unsatisfying.  Any additions, suggestions, clarifications
or comments would be welcomed.

-- Scott Purdy <spurdy@pomona.claremont.edu>, from the earlier version
   of the answer, as reposted by John Bailey <jmb184@servtech.com>

Has anyone solved (or think they've solved) Maze, a book by Christopher
Manson?  It's been driving me nuts!  There's a copy at the following URL
for those of you who want to try it out:

http://www.obs-us.com/obs/german/books/holt/books/maze/index.html

-- Cynde Callera <cyndecal@durand.com>