“Hickory Dickory Dock” is a popular English nursery rhyme. A joke was told on radio and printed in the Sheboygan (WI) Press on September 8, 1936:
 
“Hickory dickory dock…Two mice ran up the clock…The clock struck one—and the other escaped without injuries.”
     
“The clock struck one” means “one o’clock” in the nursery rhyme, but means “one mouse” in the joke.
 
A version with three mice was published in Boys’ Life magazine in August 1957:
 
“Hickory, Dickory, Dock
Three mice ran up the clock.
The clock struck one.
And the rest escaped with minor injuries.”
   
   
Wikipedia: Hickory Dickory Dock
“Hickory Dickory Dock” or “Hickety Dickety Dock” is a popular English nursery rhyme. It has a Roud Folk Song Index number of 6489.
 
Lyrics and music
The most common modern version is:
 
Hickory, dickory, dock.
The mouse ran up the clock.
The clock struck one,
The mouse ran down,
Hickory, dickory, dock.
       
8 September 1936, Sheboygan (WI) Press, “That’s That!” by W.J.P., pg. 12, col. 3:
Revise
One of the wags up in the radio department suggests this revise:
 
Hickory dickory dock…Two mice ran up the clock…The clock struck one—and the other escaped without injuries.
       
20 October 1939, Harrisburg (PA) Telegraph, “Roundabout,” pg. 13, col. 1:
Virginia Bruce’s understudy brought this one in:
 
“Hickory Dickory Dock,
Two mice ran up the clock;
The clock struck one
And the other came down uninjured.”
 
15 February 1941, Greeley (CO) Daily Tribune, pg. 2, col. 7:     
Hickory, dickory dock,
The mouse ran up the clock.
The clock struck one,
The rest suffered only minor injuries. 
 
19 February 1942, San Saba (TX) News, “I Give You Texas” by Boyce House, pg. 3, col. 6:
As Mother Hubbard did not write it:
 
Hickory, dickory, dock,
Two mice ran up the clock;
The clock struck one
But the other got away.
 
4 May 1945, The Prairie Flier  (Winfield, KS), pg. 4, col. 4:
Hickory Dickory Dock,
The mouse ran up the clock.
The clock struck one—
A hell of a lot of mice have been killed that way.
 
30 January 1950, Noblesville (IN() Daily Ledger, pg. 6, col. 1 ad:
Hickory, Dickory Dock,
Two mice ran up the clock;
The clock struck one…
But the other one got away!
(Charles L. Howard Agency.—ed.)
 
15 June 1950, Gibson City (IL) Courier, pg. 8, col. 3:
Hickory Dickory Dock,
The mice ran up the clock,
The clock struck one—
A lot of mice have been killed that way.
 
Google Books 
August 1957, Boys’ Life, “Think and Grin,” pg. 62, col. 2:
Hickory, Dickory, Dock
Three mice ran up the clock.
The clock struck one.
And the rest escaped with minor injuries.
— Danny Kemmis, Richey, Montana
 
Google Groups: rec.humor
Nursery Rhyme
Kin Blas
9/1/92
Don’t remember where I heard this one:
 
Hickory dickory dock
The mouse ran up the clock
The clock struck one
And the mouse got away with minor injuries
 
Ahsen Sabih
9/2/92
(...)
The version which I read was in MAD and it went like this.
 
Hickory dickory dock
Three mice ran up the clock
The clock struck one
Two got away with minor injuries
     
Reddit—Jokes
Posted by u/[deleted] July 15, 2016
Hickory Dickory Dock…
Three mice ran up the clock
The clock struck one
But the rest escaped with minor injuries.
 
(Something my grandfather told me when I was five)
 
Reddit—Jokes
Posted by u/killerr99 August 2, 2019
Hickory dickory dock
Three mice ran up the clock The clock struck one
And the other two escaped with minor injuries