Puzzle Corner 32

1
Puzzle Corner 32

• Hotel Morrison
• Manzarek Suite
• From an original puzzle by Barry Clarke

2
What do we know?

• Closing door
• A unlocks BE
• B unlocks CE
• C unlocks DF
• D unlocks AF
• E unlocks BD
• F unlocks CD
• There are 6 corresponding bolts on door G to be
  unlocked

3
What do we know?
A ? BE B ? CE C ? DF D ? AF E ? BD F ?
CD

• The doors A and F are entrances to the bedroom
  and door B is an exit. Lisa must alternate exits
  and entrances.
• Clearly, the minimum number of doors that need to
  be passed through is 6 (one for each bolt on door
  G). To achieve this requires each door (A-F) to
  be used only once. This is possible, and the
  required order can be deduced before going
  through any of the doors!

4
Labelling potential solutions
A ? BE B ? CE C ? DF D ? AF E ? BD F ?
CD

• Let the unknown entrance be X. With a "_"
  denoting an exit door the possible orders are
• (a) _A_F_X (b) _F_A_X (c) _X_A_F (d) _X_F_A
  (e) _A_X_F (f) _F_X_A

5
Eliminating impossible solutions
A ? BE B ? CE C ? DF D ? AF E ? BD F ?
CD

• (a) _A_F_X (b) _F_A_X (c) _X_A_F (d) _X_F_A
  (e) _A_X_F (f) _F_X_A
• Neither (a) nor (c) are possible since A must be
  followed by B or E and neither opens F.

6
Eliminating impossible solutions
A ? BE B ? CE C ? DF D ? AF E ? BD F ?
CD

• (a) _A_F_X (b) _F_A_X (c) _X_A_F (d) _X_F_A
  (e) _A_X_F (f) _F_X_A
• Since A can only be preceded by D, (e) and (f)
  are possible as DA_X_F and _F_XDA, respectively.
  With D used, door F can only be preceded by C to
  give DA_XCF and CF_XDA, respectively. Door B must
  occupy the remaining space in each possibility
  (third door is exit) so XE, but C cannot follow
  E in the former and for the latter, B cannot
  follow F. This eliminates (e) and (f).

7
Eliminating impossible solutions
A ? BE B ? CE C ? DF D ? AF E ? BD F ?
CD

• (a) _A_F_X (b) _F_A_X (c) _X_A_F (d) _X_F_A
  (e) _A_X_F (f) _F_X_A
• Since only D precedes A, (b) is possible as
  _FDA_X and (d) as _X_FDA. For (d), the exit B
  must occupy a "_" but cannot be followed by F,
  and if it is the first door, neither the C or E
  that must follow as X can be followed by the
  remaining E or C, respectively. This rules out
  (b).

8
Remaining viable solution
A ? BE B ? CE C ? DF D ? AF E ? BD F ?
CD

• (a) _A_F_X (b) _F_A_X (c) _X_A_F (d) _X_F_A
  (e) _A_X_F (f) _F_X_A
• This only leaves (b). Since D must precede A,
  only C (of the possible B,C,E) can precede F as
  CFDA_X and B must occupy the final "_" as an exit
  leaving XE.
• Hence, the final sequence must be
• CFDABE

9
The End