INTRODUCTION For some years, I have been accumulating these numerical phrases, like 26 L o t A , and my list of them had reached 35 pages when I received the following history from Mike Sklar. It comes from the Usenet newsgroup rec.puzzles, under language/english/meaning/equations.s , with Will Shortz's first 24 examples under language/english/meaning/equations.p . Incorporating these extended this list to 47 pages. Adding material from William Hartston's Book of Numbers extended this to 54 pages. Adding other material, mostly from an email from Hartston extended this to 62pp. The present version is 84 pages long, with 66 pages of examples.
CONTENTS Introduction. Morgan Worthy's material 1
Main List 5
The Almanac of Cards 71
The Evangelists Rhyme 71
A German Counting Rhyme 72
The Magpie Rhyme 73
The Months Rhyme 73
A Sneeze Rhyme 74
Cumulative Number Games/Songs 75
Will Shortz's original examples 81
Unsolved and Unclear Examples 82
MORGAN WORTHY'S MATERIAL Morgan Worthy (http://mworthy.home.mindspring.com/) originated the puzzle form now called "linguistic equations." The first ones were published in his 1975 book, Aha: A Puzzle Approach to Creative Thinking; Nelson Hall, Chicago, 1975 now out of print.
Here are his comments on how he thought of the idea in the first place, and why they have become such perennial favorites.
I got the idea for linguistic equations from graffiti someone had written in the form of an obscene formula on a restroom wall at the University of Florida. When the answer suddenly came to me, I realized the format was a good one for eliciting the "aha effect". After that I used such items as exercise material when teaching workshops on creative thinking.
My guess is that one reason a person enjoys linguistic equations is that the answer hits him or her all at once rather than being solved in an incremental fashion. It is similar to what happens when we suddenly see an embedded figure pop into focus; the satisfaction is visceral rather than just intellectual. My experience was that people often had the answer to an item come to them when they were not consciously thinking about the puzzles, but relaxed, such as in the shower or about to fall asleep.
Another factor is that with well written items, success does not hinge on obscure information. Ideally, a person should never have to feel, "I could never have gotten that one no matter how long I worked on it." There is something ego enhancing about knowing you have the answer inside and just need to find it.
Following are some of the original linguistic equations from this book. [I have spaced them out a bit.]
(1) 8D. 24H. = 1W.
(2) 4J. + 4Q. + 4K. = all the F.C.
(3) T. = L.S.State
(4) 23Y. 3Y. = 2D.
(5) C. + 6D. = N.Y.E.
(6) S.R. of N. = 3
(7) 1 + 6Z. = 1M.
(8) B. or G. F. M. = O.
(9) " R. = R. = R."
(10) Y. + 2D. = T.
This puzzle form reappeared as 24 "equations" by Will Shortz, printed in the May June 1981 issue of Games magazine, with an acknowledgement to Morgan Worthy [at the end of the answers]. Games ran several followups in subsequent issues, and reported that people kept resubmitting the puzzle to them, sometimes as original work! Many people have now added to the list of equations. The 24 original ones are starred (*) below. [One * is omitted, on 64 S o a C. I have indicated these by S1 in my listing.]
A few more comments are needed about the esthetics of this type of puzzle in addition to those of Morgan Worthy above. A good letter equation emphasizes the uniqueness of the number on the left hand side of the equation, and is not merely one in a long series of equations. For example, the equation 8 = AN of O = Atomic Number of Oxygen is excluded from the following collection, along with equations involving atomic weights, levels on some scale, years in which well known events occurred, etc. Also, the left hand side must be an exact integer, thus 18.5 = ME from the WT = Minutes Erased from the Watergate Tapes is excluded, along with fundamental constants, non integral conversion factors between units of measure, well known dimensions, etc.
Finally, we finish with one matter of convention. If a number occurs on the right hand side of the equation, it is spelled out (as in 1 = B in the HWT in the B = Bird in the Hand Worth Two in the Bush).
There follow 9 pages of examples. I have now incorporated them into my list below. The format used in the Usenet list is shown in the examples given already and in
1 = D at a T = Day at a Time
but I find this awkward as the = signs cannot be read as 'equals', and so I have converted them all into my format which is:
1 D a a T Day at a Time.
In Feb 2000, I acquired a copy of the Handy Books, edited by Lynn Rohrbough for Cooperative Recreation Service, Delaware, Ohio. This contain 20 booklets, called Kits. In Kit E: Mental Games Brain Teasers, Testers, Puzzles and Word Games; 1927, pp. 15-16 is Numerical Nut Test which has 100 numerical phrases to be completed. E.g., no. 1 is The (3) Musketeers. You can produce a version with the (3) replaced by a blank space and then distribute copies as a party puzzle or read them aloud for people to state or write the answer. Though not of our type, I found this a useful source of examples.
I have compiled my list from a number of different lists and I have extensively extended it by looking in various appropriate reference books. In particular, I have included almost all forms like 3 F i a Y (Feet in a Yard) that I have come across. Different sources provide these in somewhat different formats _ I have generally standardised them. Morgan Worthy and the rec.puzzles list editor have made pertinent comments about the aesthetics of these phrases, but many setters have made examples which do not follow the rules and a number of the items in the rec.puzzles list seem to violate the rules. So I have included everything which occurs in any list that I have seen and anything similar that I have come across. NOTE that several of the measures used in the past varied depending on locale and on what was being measured _ e.g. a firkin or a hogshead was quite different depending on what was being measured or where it was being measured _ and some were never standarised and have varied with time, so that some entries contradict one another! For examples, a hogshead of wine had seven sizes, varying from 30 to 93 gallons, depending on the kind of wine! However, Chapman gives hundreds of obscure units, so I have decided against trying to include all of them.
Thanks to Richard Armitage, Laurie Brokenshire, Jack Caunter, James Dalgety, Simon Dickerson, Harriet Hall, Tom Henley, Eric Korn, Simon Nightingale, Tim Rowett, Mike Sklar and Andrew Turnbull for lists. William Hartston has given me some answers for previously unsolved examples and has proposed the name 'ditloid', deriving from the example 1 D i t L o I D, qv. Thanks to David Beamish for solving a number of intractable examples.
The last pages contains unsolved examples _ the original formats are retained for unsolved cases. I would be grateful for solutions to the unsolved examples and for other lists or entries.
In Aug 2003, I thought to use Google, etc. to get information about a number of examples whose solutions were unclear to me. This clarified about 60 entries and they are now amended. I have indicated entries where Google gave no useful information by 'Nothing on Google'. In some cases, Google only directed me to one of the lists of such phrases and I have indicated this by 'Google goes in circles'. This searching also led to several websites which seem to be related to U, one of which I have now entered as U2. Another is http://freespace.virgin.net/mike.jacqueline/exx.htm/ where xx is the number desired, e.g. 01. After about 20, the entries are combined. There are very few numbers over 100. These pages do not show up on the site's contents page.
SOURCES Christine Andrews (St Peter & St Paul R. C. Primary School, St Pauls Wood Hill, Orpington, Kent, BR5 2SR). Unheaded Easter holiday quiz, 2pp, 51 examples. Supplied by Tom Henley.
Richard Q. Armitage. Message posted to NOBNET on 7 Jan 1999. 23 unsolved examples from a set of 150 which I've asked him to send. 23 solutions given in a posting on 27 Jan.
Colin R. Chapman. How Heavy, How Much and How Long? Weights, Money and Other Measures Used by Our Ancestors. Lochin Publishing, Dursley, Gloucestershire, (1995), slightly revised, 1996.
Chester World Scout Jamboree Fund-Raising Committee. 1994? 100 examples. I have requested the answers.
Amy Daw. Numbers Quiz. To raise money for her trip to Iceland. 100 examples. Closing date 1 May 1999. From James Dalgety.
Heather Dickson, ed. The Bumper Compendium of Mind-Bending Puzzles. Lagoon, 1998, chapter 8 (unpaginated). 19 examples with answers.
GR. Games Readers. Equation analysis tests. Repeats S1 and gives a new set of 24. Answers on p. 126. However, my source, Tim Rowett, did not have the answers and the copy provided does not indicate the issue and only shows p. 64 on it.
General Knowledge Quiz to sponsor a walk in 1999 by Verity Spencer from the Dead Sea to the Red Sea in Aid of the Foundation for the Study into Infant Deaths. 1998. 50 examples. From Simon Nightingale via Tim Rowett. Solutions from Verity Spencer.
H. William Hartston. The Book of Numbers. Richard Cohen Books, London, 1997, 218pp. This is full of numerical information and trivia. Though not presented as numerical phrases, many entries can easily be made into numerical phrases and I recognise a number of examples used in other recent sources as being derived from this. I will cite this as H _ since the entries are in numerical order, there's no need to cite the page. I won't cite him for every item he mentions as he mentions about a third to a half of what I have. Generally I cite him when a new entry is based on him and I sometimes cite him when he gives further details or confirms an unusual fact.
H2. William Hartston. Email message of 18 May 1999 with 296 examples (but 4 were repeated), many used in his Independent column. These are in simple form, like: 1 Day in the Life of Ivan Denisovich and I have adapted them to my form. I will cite these as H2 with new examples cited as H2-new. 150 examples were new!
[William Hartston?]. Numbers. The Independent (2 Dec 1994).
How Long Will This Test Take You? Anonymous sheet with 23 examples.
KK. Keith Kay's Word Riddles. Sheet with 22 examples, provided by Tim Rowett, Dec 1999. Most of these are common, so I will only cite this for unusual examples. He often precedes his examples with 'There are', but I have not considered this. He gives the number of letters in the word after the initial, but several are incorrectly counted.
"Lemon, Don" [pseud. of Sheldon, Eli Lemon]. Everybody's Scrap Book of Curious Facts. A Book for Odd Moments. Saxon & Co., London, 1890. Pp. 12-13 is a section on Bible Statistics, which he says were compiled by the Prince of Granada, heir to the Spanish throne, who was imprisoned for 33 years with no companion but his Bible. P. 48 is a section on Ancient Alphabets. Pp. 213-215 is on Magic of Numbers.
NQ. Numbers Quiz. From Tim Rowett, Mar 2001. 100 examples with answers, some amended by Rowett. These sometimes have awkward grammar. The answers are labelled Quiz Sheet 468.
P. Graham Perry. The Numbers Game. Warner, 1993. This has 226 examples which I have entered here. Perry presents them as. e.g. 24 = h. in a d. Pxx will denote items in Perry on p. xx and Pxx-new will denote new items from Perry.
Leighton Rees. On Darts. Atheneum, NY, 1980. On pp. 18-22, he gives darts vocabulary which includes many numerical phrases similar to bingo calls.
R.Lynn Rohrbough, ed. Handy Books, Cooperative Recreation Service, Delaware, Ohio: Kit E: Mental Games Brain Teasers, Testers, Puzzles and Word Games; 1927; Numerical Nut Test, pp. 15-16. 100 numerical phrases to be completed.
S1. Will Shortz. Equation analysis test. Games 5:3 (No. 23) (May June 1981) 25. 24 examples, marked S1 in the list below. I've gathered them in their original format at the end of the Appendix.
S1,S2. Will Shortz. Equation Analysis Test # 1 and # 2. IN: Will Shortz's Best Brain Busters; Times Books (Random House), 1991, pp. 34, 86, 118, 125. Two sets of 24 examples, the first set being the set just mentioned, marked S1 below. The second set will be marked S2 below. I also have this on a photocopy with another set of 48 typed out, almost all taken from the Shortz examples, dated 1984 _ this came from Jerry Slocum, via James Dalgety.
S3. Will Shortz. Equation Analysis Test. From the New York Times. No other details, but has a date of 6 May 2000 on it; sent as an email on 31 May to Eric Korn who kindly gave me a copy. 22 examples, no solutions, but we have found 21 which seem correct.
Teasers. Unidentified sheet with 57 examples, with hints sheet, but no answers. All examples are standard, but sometimes slightly different than what I had before.
Templewood School. c1993? 100 examples. I have the answers. Provided by Tim Rowett.
The Ultimate Test (Revisited). Anonymous sheet, with ref: Ib/6.Ut date: 01 12 90 at the bottom. 39 examples.
U. Usenet newsgroup rec.puzzles. An 11 page document (when reformatted like the present) with about 534 examples. I will denote these by U at the end of the solution. Examples which are new will be denoted U-new.
U2. website: http://rec puzzles.org/sol.pl/language/english/ . A 5 page document (when reformatted like the present) with about 245 examples in the form of U and mostly included in U. 35 of these are either new or variations of the U entry. I will enter these 35 and denote them by U2. I found this in Aug 2003, but it seems old.
MAIN LIST T R F's The Roaring Forties
H 'n' O D Hundred 'n' One Dalmatians
00 n I D C f n A new International Dialling Code from next April
0 M A a (W S) Much Ado about Nothing (William Shakespeare). U new. M A a 0 is better.
0 O f M B No Orchids for Miss Blandish (detective(?) novel). U-new.
0 P L H No Place Like Home. H2-new.
0 P o a B T Pockets on a Billiards Table
0 S B i a S Swim Bladders in a Shark. U-new.
0 S C i H Snowball's Chance in Hell. U-new. (Not really a numerical phrase.)
0 S L S Nothing Succeeds Like Success. H2-new.
0 W o m W Wheels on my Wagon (Line from Three Wheels on my Wagon, qv.)
H B ½ His Better Half. R46-new.
B t S 1 Back to Square 1
H i 1 Hole in 1
T O M H P 1 This Old Man, He Play One, ...
T W 1 The Wild One (film title)
1, 2, B M S Buckle My Shoe
1, 2, 3, 4, J a t C D Jenny at the Cottage Door. [Robert Ford; Children's Rhymes Children's Games Children's Songs Children's Stories. A Book for Bairns and Big Folk; Alexander Gardner, Paisley, 2nd ed, nd [1904 _ BL], p. 53.]
1, 2, 3, 4, 5, 6, 7, A G C G t H
All Good Children Go to Heaven. [Robert Ford; Children's Rhymes Children's Games Children's Songs Children's Stories. A Book for Bairns and Big Folk; Alexander Gardner, Paisley, 2nd ed, nd [1904 _ BL], p. 53.]
B I W 1 a 20 But I Was 1 and 20 (A Shropshire Lad)
1 a a T at a Time
1 A B Armed Bandit. H2.
1 A i A F D April is April Fool's Day. U-new. H2.
1 A N o H Atomic Number of Hydrogen. H2-new.
1 a P 2 a P H C B 1 a Penny, 2 a Penny, Hot Cross Buns (If you have no daughter, Give them to your sons, If you have none Of these little elves, Why then you must eat them All by yourselves)
1 A W o H Atomic Weight of Hydrogen
T G 1 B To Go 1 Better
1 B B i t L Bonus Ball in the Lottery. H2-new.
1 B i t H W T i t B Bird in the Hand Worth Two in the Bush. U-new. (I think it is usually: A Bird in the Hand is Worth Two in the Bush.)