[Index]
Reproduced here are various Mathematical Puzzles from
The Old Farmer's Almanac,
published continuously since 1792. All copyrights hereby acknowledged.

I finally got around to
scanning selected content from the 1986 issue of The Old Farmer's Almanac.
The "Old and New Mathematical Puzzles" feature was always my favorite, so that's
what is posted first. Difficulty levels are assigned as 1 for the easiest to
5 for the hardest. Solutions are provided for levels 1 through 4, but level
5 (problems 12 through 15) problems were to be mailed in (no email in the day)
to vie for a cash prize for providing the "best set of solutions," though I
don't know how one solution to these problems can be deemed "better" than another.
Problem #5 is interesting in that you must assign a value for the various numerical
prefixes and quantities. Sure, we all know what "atto" and "score" are, but
what about "crore" and "myriad?"
Old and New Mathematical Puzzles
Blanton C. Wiggin, Puzzle Editor
From an above average group of readers' puzzles, we have selected 15 classical,
original, or timely puzzles for 1986. They are graded for difficulty, so that
there should be something of interest for everyone. We hope you find them challenging.
No calculus, computers, or tricks. We try to include specialized knowledge,
if needed, in the puzzle statement. Some puzzles may require a chart or table
of data from your local library.
We will award one prize of $50 for the best set of solutions to puzzles 12
through 15 received before February 1, 1986. The answers to these four are omitted
here.
We use a point system to judge the prize set. A basic, unadorned, correct
answer is 20 points; for a thorough analysis, an elegant or novel answer, up
to 5 points extra. Numerical errors lose only 2 or 3 points, if it is clear
that the method is understood.
Explanations and Prize  Set Answers will be sent after June 15 to anyone
sending 50ยข and a selfaddressed stamped envelope to "Puzzle Answers," The Old
Farmer's Almanac, Dublin, New Hampshire 03444.
We will also. pay $15 for any original puzzles we use in The Old Farmer's
Almanac for 1987. Closing date for submissions is March 1, 1986. Entries become
the property of Yankee Publishing Incorporated and cannot be acknowledged or
returned. In addition to submitting a puzzle, please tell us the type of puzzle
you like best, such as magic squares, geometry, timeratequantity, mazes, logic,
number substitutions, etc.
From a large group of good answers, we are happy to announce a secondtime
winner for 1985: Arthur Loepp of Kansas City, Missouri, with 97 points repeating
his 1982 win.
Runnersup were Leon Kreidler, Sheboygan, Wisconsin, last year's winner,
95 1/2; Tina Virzi, Plattsburgh, New York, 93 3/4; and Harvey Vigour, Waynesboro,
Virginia, 93.
Other high scorers were G.M. Hall, Alexandria, Virginia, and past winner
Newton Amos, St. Louis, Missouri.
Congratulations to all! Have a go at these 1986 puzzles and send your answers
early for puzzles 1215. Use a separate sheet for each puzzle or answer, and
be sure each sheet has your name and address on it. Good luck!
1. Less Housing
Difficulty: 1
a. Relocate only 2 walls (toothpicks) and reduce 5 rooms to 4.
b. A developer agreed to put in 5 roads with 4 houses on each road. The planning
board allowed only 10 houses, yet he successfully completed his agreement. How?
William W. Hurley: Princeton, W Va. and Paul Fidelet, Sudbury, Mass.
2. The Scrambled Salesman
Difficulty: 1
An egg salesman sold his first customer half his crates of eggs and half
a crate more. His second and third buyers took the same type of order. He filled
all 3 orders, was sold out, and hadn't had to break a single egg or crate all
day.
How many crates had he sold?
Jennifer Hughes, Pinconning, Mich.
3. Muffin Madness
Difficulty: 2
Milly Miffen made a muffin more than Molly Murphy's mother Mabel made. Milly
Miffen's mother Maida made a muffin more than Molly Murphy made. Milly Miffen,
Molly Murphy's mother Mabel, Molly Murphy, and Milly's mother Maida Miffen made
50 muffins, but Milly Miffen and Molly's mother Mabel Murphy made four muffins
more than Molly Murphy and Milly's mother Maida Miffen made. So murmur now how
many muffins Milly made.
Jerry Curtright, Carpemersville, Ill.
4. Third Millenium Lady
Difficulty: 2
Julie will be X years old in the year X^{2}.
Her uncle was Y years old in the year Julie was born, having been born back
in Y^{2}!
When were niece and uncle born?
Rand Higbee, White River, S. Dak.
5. Curious Counting
Difficulty: 2
So you think you learned to count when you were three or so? Maybe, but do
you know these quantities  nouns or prefixes for cardinal numbers? All are
part of the English lexicon, just as "score" is 20.
ace __________________
atto __________________
avogadro __________________
brace __________________
bundle __________________
centillion, AngloGerman __________________
centillion, FrancoAmerican __________________
crore __________________
duodeci __________________
e __________________
femto __________________
fin __________________
giga __________________
icosa __________________
lakh __________________
long hundred __________________
love __________________
K __________________
megamicro __________________
myriad __________________
nano __________________
nonad __________________
pi __________________
pico __________________
ream, standard __________________
googol __________________
grand __________________
great gross __________________
heptad __________________
hexadec __________________
shock __________________
tera __________________
thou __________________
tre __________________
undeci __________________
zip __________________
Some are used only in special fields, of course, but they all have a dimensionless,
fixed numerical value. They do not represent physical properties, such as a
gallon is so many quarts (volume), or milesperhour so many knots (speed),
which have physical dimensions.
Jackie Shoemaker, Waverly, Penna.
6. Dense Pack
Difficulty: 3
Tom is stacking perfectly round logs in a certain rectangular space, and
he wants to pack them as tightly as he can with all the logs exactly the same
diameter. Will the stack be more dense if he uses logs of smaller diameter or
greater diameter?
Bill MacCartney, Ashby, Mass.
7. Triplets Hop
Difficulty: 3
Jigsaw and Sawjig are 6digit numbers. If 6 times Jigsaw = 7 times Sawjig,
what is the value of each letter?
Peter Voorheis, Friendship, L. I.
8. Almanacryptogram
Difficulty: 3
a. Work out these anagrams about 1986. Ignore the underlinings for now.
YELLAH STRUNER HITS RAYE
b. Using the new letters falling into the underlined positions, make a related
word in the numbered spaces.
___ ___ ___ ___ 1
2 3 4
c. Put these letters into the numbered spots in this cryptogram. They may
also go elsewhere. Solve.
V UQZ1Y WDSGT2KK QD WSPINXZD WL3XW KQLX WYBYMY V WPHXZ WHXAIVA4X CVLXW.
Erma Nightingale, Newton Highlands, Mass.
9. Squares, Cubes, and Factors
Difficulty: 4
a. A certain characteristic enables a number to be both a perfect square
and a perfect cube, How many such integers are there less than one million?
b. What is the smallest integer which is the sum of two cubes, in two different
ways?
c. Is there an integer less than b. which, squared, is the sum of two squares,
in four different ways?
d. What is special about the number 2520?
John H. Hitchcock, Princeton, Mass. and Richard Burgess, Lonoke, Ark.
10. Deductions
Difficulty; 4
Each offour men was given a similar appearing closed box, and the contents
list of one of the other boxes. Each box contained 3 colored balls in unique
assortments:
BBB; BBW; BWW; WWW
Each man knew this, saw only the one list, but in turn opened and announced
the first two balls he withdrew from his box. He then tried to deduce the third,
still unseen color in the box.
Said Art, "I drew 1B, 1W, and I know the third."
Bob: "I pulled out 2B, and I know the third."
Cal announced he had 2W, third unknown.
Don was blind, but correctly announced his 3 and all other remaining colors.
What were they? /p>
John A. Robbins, Falmouth, Mass.
11. Missin' Digits
Difficulty: 4
Fill in the blanks. The answers can be reasoned out. No lefthand zeros,
please.
Dorothy J. Johnson, Brookfield, Wis.
12. Quadrant Square
Difficulty; 5
Just as I, II, III, IV describe triggeometric quadrants, they can be the
starting numbers for an 8order magic square. All horizontals, verticals, and
major diagonals add to the same number. Each 4square quadrant adds similarly
to a number. Use the quantities 5 to 64 once and only once in the empty boxes.
Alvis King, Orleans, Ind.
13. Scrolling Digits
Difficulty; 5
Scrolling signs are like the one on the old Flatiron Building in Times Square,
New York, continuously stepping to the left in a long loop before repeating.
Here are some numbers which scroll to the right one place and stop.
IMAGE HERE
Question: What series of digits, when multiplied by 6, scrolls?
Have some fun with this simple new concept. Your answers and whatever else
you discover about scrolling will be considered in your Prize Set answer.
Gary Baird, Carthage, Mo.
14. Heptagon Hex
Difficulty; 5
With center at O, describe circle of diameter AH. Using A and H as centers,
and radius AH, construct arcs intersecting at I.
Now draw any straight line through A except concurrent with AH or AI. Mark
off 7 equal segments ending in A'.
Draw A'H and construct parallels from AA', dividing AH into 7 equal segments
at B, C, D, E, F, & G. Construct IC and extend to circle O at J. Using chord
AJ as a length, construct equal chords JK, KL, LM, MN, etc.
What have you drawn?
Norton Black, Tucson, Ariz.
15. Cross Number A
Difficulty: 5
a. Many people like crossword puzzles, so here are a pair of analogous stumpers
using only numbers. Same rules. Any numbers too long for the space are rounded
in normal fashion to the nearest value. Please ignore decimal points.
Across
1. Mantissa of log
5. 370 squared
9. MDXXVII
10.April 24's day of 1986
11. This digital root = 0
12. Old long distance
13.This digital root = 1
15. 4th root of 614,656
16. East Boston (Mass.) zip
18. Hexadecimal base
19. Product of 2 primes each ending in 1
21. A lakh
23. Hastings' binary year
225. Consecutive digits
26. Odometer showing a seventh of the square root of 240,100
27. Unlucky number
28. Hollywood (Calif.) zip
30. Duodecimal base
32. New emergency #
33. 164 in duodecimal
34. End of T'ang Dynasty
35. Semicircle degrees
36. Pearl Harbor minus 30
37. mm/100 inches plus inches/10 kilofeet plus a score
38. IV x MCLXXVII
Down
1. pi
2. 517 x 2 x 71 x 205,493
3. Council of Nicaea
4. 25th prime above 1
5. Perfectsight year in binary
6. Last day, last century, British style
7. Bigquestion value
8. 1/99
12. pounds/kilogram
14. Battle of Sekigahara
16. West Springfield (Mass.) zip

17. Triply palindromic zip
20. American commercial jet
22. Certain Korean commercial flight
23. When Balboa died
24. Labor Day 1986, computer style
29. 6squared in quaddecimal
31. e
34. Largest 3digit prime
35. 11 in hexary
39. 9 in quinary

b. Topsyturvy Cross Number
This puzzle works both rightsideup and upsidedown. Thus you can use only
0, 1, 6, 8, or 9. No lefthand (leading) zeros, such as
06, permitted. No digit appears more than 3
times in either orientation. No singledigit numbers.
Sorry, but we lost some of the clues and clue numbers! Not to worry; these
are all you need:
a. The year of this OFA.
b. Product of two numbers in the puzzle.
c. 1 across, 4 across, 12 across, and 14 across have a common factor
larger than this.
d. There is only one perfect square.
Samuel W Eliot, Oklahoma City, Okla. and Bob Lodge, Seattle, Wash.
Answers to Old and New Mathematical Puzzles
1. a.
b.
2. 7:4, 2, & 1.
3. 14
4. 1980, 1936
5. 1, 10^{18},602 X 10^{21}, 2, 10^{3}, 10^{600},
10^{303}, 10^{7}, 12, 2.718,10^{15}, 5, 10^{9},
10^{100}, 10^{3}, 1728, 7, 16, 20, 10^{5} 120, 0, 10^{3},
10^{6}, 10^{6}, 10^{4} 10^{9}, 9, 3.142, 10^{12},
500, 60, 10^{12}, 10^{3}, 3, 0.
6. Smaller.
7.6 x 538461 = 7 x 461538
8. A dirty snowball in southern skies like SYZYGY a super spectacle makes.
9. a. 9; the sixth powers of integers 1 through 9, only.
b. 1729 = 1^{3} + 12^{3} = 9^{3} + 10^{3}.
c. Yes.
1625 = 57^{2}+1624^{2} = 400^{2} + 1575^{2}
= 825^{2} + 1400^{2} = 1113^{2} + 1184^{2}.
d. Lowest number divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
10.
IMAGE HERE
Details of reasoning in "Explanations and Prize Set Answers."
11. a. Many answers.
b. For one: 12,128,316 ÷ 124 = 97,809
1215. Prize Set. See instructions on p. 190.
See answers below 
Posted January 28, 2021
