→ Crossnumber Puzzle ←
The Little Pigley Farm
a puzzle by Bill Williams
Also known as:
Dog’s Mead, Little Pigley, Little Piggly Farm, Little Pigsby, Pilgrims’ Plot, or Dog Days
This article was written by Joel Pomerantz of San Francisco, California
in 2001 through 2006, after 2005 & 2006 correspondences with William Sit.
Date of the puzzle:
Some versions give the date of the puzzle so as to make it easier to figure out the years used in filling in the grid. I believe you, yes you, won't need this date to fill in the grid, and so I've cleverly concealed it in the Origin section of this page, in Roman numerals. Learning the year actually doesn't help very much toward solving. Just remember, you weren't hatched yesterday, and neither was this puzzle.
Use logic and algebra to solve this old English puzzle. Fill in the blanks in the "crossnumber" grid so that all answers are consistent. At the time
this puzzle was created, the English monetary system (among other
things) was quite different than today, so you may need this:
|1 pound sterling
|4840 square yards
For hints on how to begin, you can use the little graphic I put near the bottom
of the page. So as to make it harder to cheat by mistake, I've encoded them!
You probably should at least be told that dog's mead is a rectangular plot of land. Okay. You've been told. Also that no more than one numeral goes in each square. And Bob's your uncle.
1. Area of Dog's Mead in square yards
5. Age of Farmer Dunk's daughter, Martha
6. Difference in yards between length & width of Dog's Mead
7. Number of roods in Dog's Mead times nine down
8. Year that Little Pigley came into occupation by the Dunks
10. Farmer Dunk's age
11. Birth year of Farmer Dunk's youngest child, Mary
14. Perimeter of Dog's Mead in yards
15. Cube of Farmer Dunk's walking speed in miles per hour
16. Fifteen across minus nine down
1. Value of Dog's Mead in shillings per acre
2. Square of Farmer Dunk's mother-in-law's age
3. Mary's age
4. Value of Dog's Mead in pound sterling
6. Age of Farmer Dunk's son, Ed, who will be twice as old
as Mary next year
7. Width of Dog's Mead in yards squared
8. Length in minutes Farmer Dunk needs to walk one and one-third
times around Dog's Mead
9. See ten down
10. Ten across times nine down
12. One more than the sum of the digits in puzzle column
13. Length of tenure in years of Little Pigley by the Dunk
The puzzle's origin:
There has been great confusion over the years, about the origin and author of this puzzle. It's a case study in how mysteries can be created and solved.
I first saw the puzzle in 1975, under the name Dog's Mead, but it's origins go back decades earlier and to another name, The Little Pigley Farm. I learned in 2005 that the mystery was indeed solved, by one Dr. William Sit of the City University of New York, with help from many leads from other crossnumber lovers. After reading how the true author, W.T. Williams, was found, I found a biography that told some fascinating things about Williams that explain a thing or two about the puzzle.
The confusion on authorship was bound to happen. As I have now learned, the author was not an outgoing type, and—it should come as no surprise—preferred the company of dogs to that of humans. Bill wasn't the sort of person who wrangles to get credit when mistakes are published.
The puzzle has had more than one version—probably not by the same author. Published in numerous books, it was bound also to be mistakenly attributed to the the people who collected the puzzles into each volume. Ironically, it was due to mistakes in attribution that Sit finally found the author's identity.
Here is my conjecture as to why multiple versions exist. A date-specific puzzle, a few years after its creation, would no doubt tempt those of us who like to tamper toward perfection. Apparently one year after the puzzle was written, and again three years later, someone intent on keeping the puzzle current found that they could change a few things and leave the basic puzzle mostly the same, making the year current to that time. On the Web, there are versions from all three of these efforts, though, interestingly, none from the past few decades. By changing to make the current date continue to match the puzzle date, authorship became clouded. It's easy to see why the author's name would be left off, or even changed. I've certainly done it myself.
William Thomas Williams (1913-1995) created and first published The Little Pigley Farm in The Strand Problems Book, a modern anthology of perplexities and tantalizers. The book's authors are W.T. Williams and G.H. Savage. The date was MCMXXXV. Dr. Sit, of the Mathematics Department at CUNY, discovered the true author. Sit describes his detective work in detail in his 1998 paper (only available online as a PDF), On Crossnumber Puzzles and The Lucas-Bonaccio Farm 1998 . I summarize that story below.
In a typical case of lazy research, a puzzel (sic) Web site in the Netherlands (creativepuzzels.nl), attributes authorship to James Fixx, who authored several games and puzzle books including Games for the Super-intelligent (1972). The puzzle appears in Fixx's book with the name Dog Days, with the note that the puzzle "comes from Irving Hale," who was then quoted to say, "This 'cross-number puzzle' was given to me by a secretary...". The secretary, being low status and probably female, was left unnamed, sadly—probably as a result of those factors. (Why do people do that to people!?)
Michael N. Dorey, too, was credited for the puzzle, in David Singmaster's comprehensive 1996 work, Sources in Recreational Mathematics, a list that includes crossnumber puzzles printed since the first known, in 1926. Singmaster did say, however, that he couldn't trace the origin with any certainty.
Again Dorey was credited—and more plausibly, or at least for one version—in The Ticket to Heaven and Other Superior Puzzles, a 1988 book by Tom Sole. On page 92 of that book, are two clues: "The original version of this puzzle was designed by Michael H. Dorey in 1936. For this version assume that the date is 31 December 1939." (emphasis added)
From the above information, I'd say it's reasonable to guess that Williams wrote the first version, which Dorey altered the next year, and then someone changed it again in 1939, into the version which Fixx published in 1972.
Okay, so I've been saying it was Williams who wrote it, yet it was first published in a book by two authors, Williams and Savage. How did Dr. Sit discover that it was Williams? Savage wrote a Strand Magazine column called Perplexities. He may have helped the young Bill to make the puzzle a finished and publishable masterpiece, and he may have taken joint authorship for it.
Note: Strand was an English illustrated monthly, best known as the original vehicle for the Sherlock Holmes stories.
There is strong evidence that it was solely Williams who composed the puzzle. A 1956 reprinted book, Fun with Figures by L. Harwood Clarke, actually corrected their 1954 mistaken attribution:
NOTE TO SECOND IMPRESSION
I much regret that in the first impression, problem 51 (Little Pigley Farm) which was sent to me by Mr. W. A. D. Windham was incorrectly acknowledged. I understand that it was first printed in the Strand Magazine and I now express my apologies to Mr. W. T. Williams and my thanks for his permission to retain it in subsequent editions.
This is pretty clear evidence, as Sit explains:
The above acknowledgement by Clarke gave no doubt that Mr. Williams is the author even though I was not able to locate a copy of the 1935 version or the original version [in Strand].
Sit found definite evidence of Williams's qualifications, too:
[David] Wells, who had been Puzzle Editor of Games & Puzzles magazine, attributed the puzzle…directly to Williams, who composed puzzles for John O’London’s Weekly, and Savage, who published it in The Strand Magazine.
Sweetly, Sit goes on to say
According to [Clarke's] Foreword to the first impression of Fun, the other four story-line crossnumber puzzles are by Clarke himself. It seems he was as impressed as I was by Little Pigley Farm, 1935 and tried his hand on more. Indeed, he said, “The numerical cross-words will, I venture to think, be new to most readers and may encourage them to try their own skill at composing.” Amen.
Sit's “Amen” was no doubt based on the fact that Sit himself was encouraged just so. He created a very interesting and difficult crossnumber puzzle, The Lucas-Bonaccio Farm, 1998. Sit made sure to put the year of his puzzle in the title, so similar confusions were diminished.
Dr. Sit wished me to acknowledge the helpful contribution of Alastair Cuthbertson (pseudonym “Oyler”), a puzzle-maker, who confirmed the puzzle was in Clarke's book Fun with Figures .
My notes on Bill Williams, the original puzzle's author:
Intriguingly, Williams was born the same year as “Mary” in the original puzzle version. Williams was born in Fulham, London, an only child.
At the time Williams wrote The Little Pigley Farm, he was a 22 year old “academic biologist” at Imperial College. He taught at other schools in England and then moved to Brisbane, Australia in 1965. He later moved to Townsville, Australia. He apparently never married, and lived in an apartment adjoining his mother's from 1966 when she followed him to Australia, until her death, at which time their housekeeper moved into the vacated place.
His mother was an unconventional person who spent much of her life searching for the perfect religion.
Additional biographic information on Bill Williams can be found here.
Please contact me if you have any other information on the origin of the 1939 version. Or if you have any reason to believe that there were crossnumber puzzles before 1926. Or that there were story-based crossnumber puzzles before The Little Pigley Farm. (A current hypothesis is that this was the first.)
A previous request on this page turned up this intriguing bit: “My father (who was in the RAF) said it was just one of a number of 'tests' developed by the military in the 1950's to test logical thought. That may or may not be true. But what is true is that it definitely was around in 1968...I was sixteen when my father first showed it to me.” —Chris Cooke of Tamworth (England, I assume, but could be Australia)