Numerical phrases


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David Singmaster

Copyright ©2003 Professor David Singmaster

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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.

Introduction. Morgan Worthy's material 1

Sources 3

Main List 5

Appendices 71

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

Miscellany 79

Alphabets 80

Will Shortz's original examples 81

Unsolved and Unclear Examples 82

Unsolved 82

Unclear 83

Morgan Worthy ( 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.

Morgan Worthy

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 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.

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.

Clive Doig. Brainbox Puzzle Book 2. Numbers and letters, nos. 31-47, pp. 18-19.

Equations. Anonymous sheet with 21 examples.

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 . 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.
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

007 J B James Bond

H a L i B t 0 Half a Loaf is Better than None

I G P o 0 I Got Plenty o' Nothing (Gershwin). H.

M A a 0 Much Ado about Nothing (Shakespeare)

0 B i a E T Bones in an Elephant's Trunk

0 B L S B Business Like Show Business. U-new.

0 C i a G o W Calories in a Glass of Water

0 D C a w W F Degrees Centigrade at which Water Freezes

0 D o L a G Degrees of Longitude at Greenwich

0 i L i T is Love in Tennis

0 H Zero Hour. H2-new.

0 M Zero Mostel (the actor). U-new.

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[1903] _ 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[1903] _ 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.)

1 B o a A Breast on an Amazon

1 C 2 i D 3 i C S a C 1's Company, 2 is Dreary, 3 is Company, Safe and Cheery (Stephen Sondheim: Company)

1 C A i M Carbon Atom in Methane. U-new.

M f D b n 1 C f T Millions for Defense, but not One Cent for Tribute. R97-new. (Said by some American leader when the Barbary pirates demanded tribute money, c1820.)

1 C i an A Cell in an Amoeba. U-new.

1 D a a T Day at a Time. S2. U.

1 D i t L o I D Day in the Life of Ivan Denisovitch. [By Solzhenitsyn.] P44-new. (H & H2 have Denisovich.)

1 E D i a L Y Extra Day in a Leap Year. H2-new.

1 E J Eyed Jack(s) (One Eyed Jacks was a film by Brando.)

I t K o t B t 1 E M i K In the Kingdom of the Blind the 1 Eyed Man is King (H. G. Wells)

1 E M i K i t C o t B Eyed Man is King in the Country of the Blind. H2-new.

1 E 1 H F P P E One Eyed One Horned Flying Purple People Eater (pop song, c1950s)

1 E o a C Eye on a Cyclops. P50. U.

1 E o a M S Edge on a Möbius Strip

1 E o C Eye on Cyclops

1 E O H F P P E One Eyed One Horned Flying Purple People Eater (pop song, c1950s). U-new.

1 f A a A f 1 1 for All and All for 1

1 F b 1 H Z i a G Followed by 1 Hundred Zeroes is a Googol

1 F b 100 0s i a G Followed by 100 0s is a Googol

1 F b 100 Z i a G Followed by 100 Zeroes is a Googol

1 F b O H Z i a G Followed by One Hundred Zeroes is a Googol. U-new.

1 F D Fine Day (translation of Un bel' di, in Madame Butterfly)

1 F i t G Foot in the Grave. U. H2.

1 F o t C N One Flew Over the Cuckoo's Nest. (novel by Ken Kesey). U. H2.

1 f S for Sorrow (Magpie rhyme, see Appendix.)

OR Fell Swoop

1 f t M 2 f t S 1 for the Money, 2 for the Show

1 f t R for the Road

T A S f 1 G The Ace Stands for 1 God. (The Card Almanac _ see Appendix.)

1 G L f M Giant Leap for Mankind. U-new.

1 G T D A Good Turn Deserves Another. U. H2.

1 H o a D Hump on a Dromedary

1 H o a U Horn on a Unicorn. U. H2.

T W 1 H S The Wonderful One Horse Shay. R25-new. (Poem by Oliver Wendell Holmes(?).)

1 H T Horse Town. H2.

1 i a L N One is a Lonely Number (1972 drama based on a story by Rebecca Morris). H

1 i b L a 2 i b S 1 if by Land and 2 if by Sea (Paul Revere's Ride). P38, U give the two parts separately.

1 i 1 a A A is 1 and All Alone (Green Grow the Rushes 0h _ see Appendix)

1 i 1 a A A a E S B I S is 1 and All Alone and Evermore Shall Be It So (Green Grow the Rushes 0h _ see Appendix)

1 i O a A A is One and All Alone. H2-new. (Green Grow the Rushes 0h _ see Appendix.)

1 i O a A A a E S B I S is One and All Alone and Evermore Shall Be It So (Green Grow the Rushes 0h _ see Appendix)

1 i t L N One is The Loneliest Number. P19-new. U. (Opening line of One, by Nillson.)

1 K E (B) Kelly's Eye (Bingo). U-new. (Rees gives it as darts slang.)

1 K K o t E S B King Kong on the Empire State Building. P7-new. U. (Not really a numerical phrase!)

1 L f t R, A f t P Law for the Rich, Another for the Poor. H2.

1 L i a M Lens in a Monocle

1 L o a C P Length of a Cricket Pitch (in Chains)

1 L t L Life to Live. S3-new.

1 M 1 V 1 Man, 1 Vote

1 M a h D Man and his Dog

1 M a h D W t M a M Man and his Dog Went to Mow a Meadow. H2-new.

1 M B Man Band. H2.

1 M i a S D J Mile is a Sabbath Day's Journey. Chapman, p. 24, citing Acts 1:12.

1 M L o t C F Maple Leaf on the Canadian Flag. (There is a use of this on Google.)

OR ?? More Lap on the Chequered Flag. Nothing on Google, though 'One more lap' is common.

1 M M i A M P Man's Meat is Another Man's Poison. H2-new.

1 M o t E Moon of the Earth

1 M R t C More River to Cross

1 M W t M Man Went to Mow. NQ89.

1 M W t M a M Man Went to Mow a Meadow

1 M W t M W H D Man Went to Mow With His Dog. U-new.

I H 1 N It Happened One Night (film title)

1 N S Night Stand

1 N u G Nation, under God (part of US Pledge of Allegiance)

1 O t E Over the Eight. U-new.

1 o O A i M One of Our Aircraft is Missing (1941 film). H.

1 P = 1 KW 1 Picture equals 1 Thousand Words

(1 Kiloword = 1000 Words)

G i 1 P C I a 99 P C P Genius is 1 Per Cent Inspiration and 99 Per Cent Perspiration (Thomas Edison)

1 P i a P T Partridge in a Pear Tree. H2.

1 P o E Pair of Eyes

1 P W A Paper Wedding Anniversary (Brewer says this is the second anniversary.)

1 Q B i a H Queen Bee in a Hive

1 R A in E B Rotten Apple in Every Barrel GR-new. Solution from mike.jacqueline website.

F 1 R C Formula 1 Racing Car

1 R i a F M Referee in a Football Match

1 R i a M Referee in a Match. (The above version is better.)

1 S C i D P Single Calorie in Diet Pepsi

1 S D M a S Swallow Doesn't Make a Summer. U-new.

1 S d n M a S Swallow does not Make a Summer

1 S F 2 S B 1 Step Forward, 2 Steps Back

1 S o a M S Side on a Möbius Strip. U.

1 S S Singular Sensation. P15-new. U. (Song from A Chorus Line)

OR Stop Shopping. From mike.jacqueline website.

1 S S f a M Small Step for a Man (Neil Armstrong, on the Moon). U. H2.

1 S t a M S Side to a Möbius Strip

1 S t K T B Stone to Kill Two Birds. H2-new.

1 S U P i a B Stroke Under Par is a Birdie. U-new.

1 T a A Thing after Another. H2-new.

1 T B m S Two, Buckle my Shoe. H2-new.

1 i t L N One is The Loneliest Number. P19-new. U. (Opening line of One, by Nillson.)

1 T M Track Mind

1 T o a M Track on a Monorail

1 T O K Time Opportunity Knocks. P12-new.

1 T R p Y Tree Ring per Year. U.

OR Tax Return per Year

1 T t O K Time that Opportunity Knocks. U-new.

1 t W a 1 t P 1 to Watch and 1 to Pray (Thomas Ady, 1655. See Appendix.)

1 U P f a B a G Under Par for a Birdie at Golf. H2-new.

1 W o a U Wheel on a Unicycle. S1. P cover, i, 14. U. H2. NQ85.

1 W o a W B Wheel on a Wheel Barrow

1 W o m W Wheel on my Wagon (Line from Three Wheels on my Wagon, qv.)

1 W S Way Street

1 W T Way Ticket. H2.

1/T Once upon a Time

1 Z i a G o S Z in a Game of Scrabble. NQ99-new.

A B B f 2 A Bicycle Built for 2

M Y B f 2 Make Your Bed for 2 (Translation of Greek song title from

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