The mushroom is the subject of a popular riddle:
 
Q: What room can no one enter?
A: A mushroom.
 
The riddle has been cited in print since at least 1925.
 
 
9 August 1925, Roland (IA) Record, “Riddles,” pg. 2, col. 1:
What room can no one enter?
A mush-room.
 
Google Books
Railway Carmen’s Journal
Volumes 39-40
1934
Pg. 188:
What room can no one enter? — A mushroom
 
22 March 1936, Boston (MA) Herald, “Letters From Members: Who Knows More Riddles?.” pg. 10B, col. 8:
What room can no one enter? Answer: A mushroom.
(...)
JEANNE WRIGHT.
 
1 May 1936, The Times of India (New Delhi), pg. 20, col. 2:
What room can no one enter?—A mushroom.
 
12 January 1941, Boston (MA) Herald, “Good Riddles, Jean!,” pg. 12B, col. 4:
Q.—What room can no one enter?
A.—Mushroom.
(...)
JEAN KAPLAN.
 
Google News Archive
9 April 1941, >i>The Age, (Melbourne, Australia), “Riddles,” Junior sec., pg 14, col. 5:
What room can no one enter? A mushroom.
     
13 May 1950, Chicago (IL) Defender, “Mail Bag,” pg. 24, col. 6:
Here is a riddle: What room can no one enter? (Answer—A mushroom).
 
10 August 1957, Journal and Guide (Norfolk, VA), “Jay-Gee Riddles,” pg. 12, col. 8:
Question: What room can no one enter?
Answer: A mush-room.
 
Google News Archive
28 February 1962, The Free Lance-Star (Fredericksburg, VA), “Fun Time—The Riddle Box,” pg. 11, col. 2:
What room can never be entered?
A mushroom.
 
Google News Archive
3 January 1966, Deseret News (Salt Lake City, UT), “Fun Time—The Riddle Box,” pg. 8B, col. 4:
What room has no walls, floors, or doors?
A mushroom.
 
Google News Archive
24 August 1968, Deseret News (Salt Lake City, UT), “Fun Time—The Riddle Box,” pg. 2B, col. 4:
What room can no one enter?
A mushroom.
 
Google Books
Games to Improve Your Child’s English
By Abraham B. Hurwitz and Arthur Goddard
New York, NY: Simon and Schuster
1969
Pg. 97:
What room can no one enter?
A mushroom.
 
Google Books
Five Men Under One Umbrella:
And Other Ready-to-Read Riddles
By Joseph Low
New York, NY: Macmillan
1975
Pg. 35:
What room has no walls, no floor, no window, no door?
A mushroom.
 
Google News Archive
2 December 1975, The Free Lance-Star (Fredericksburg, VA), “Fun Time—The Riddle Box,” pg. 18, col. 1:
What roo mcan no one enter?
A mushroom.
 
Google Books
The Silly Riddle Book
By Robert W Alley
Racine, WI: Merrigold Press
1981
Pg. ?:
QUESTION: What room has no doors, no walls, no floor, and no ceiling?
ANSWER: A mushroom.
   
Twitter
Discreetly Greek
‏@Dgreeknalia
@AlFerretti Q:What room can you not go into??              Answ:  A mushroom ZING!
10:31 AM - 10 Apr 2009
 
Twitter
Jonathan Langley
‏@LangleyJonathan
Q: What room has no floors, no walls, and no windows? A: A mushroom! #badjoketuesday
7:49 PM - 1 Sep 2009
 
Twitter
taylor
‏@trailergale
what room can you not enter? a mushroom! hahahahahahahaha!!!
8:05 PM - 25 Dec 2009
   
Google Books
More One Liners, Jokes and Gags
By Grant Tucker
London: The Robson Press
2013
Pg. ?:
What room can’t you enter? A mushroom.