Noesis

The Journal of the Mega Society

Number 77

January 1993

EDITORIAL

Rick Rosner

5139 Balboa Blvd #303

Encino CA  91316-3430

(818) 986-9177

Evidently Chris Cole has been covering for me while I putz around.  For those of you he's told about my dad, here's the scoop:

A.  He belongs to Kaiser, which is scary all by itself, since they tend to be cost-conscious and complacent even about a F***ING HUGE LUMP in his chest, growing rapidly.

B.  After several months of x-raying lump & saying we dunno what it is, somebody decides it's an aortic aneurysm, which can blow at any time.

C.  It's a misdiagnosis, but it gets their asses moving, diagnostically.  They find that it's a recurrence of thyroid cancer from 1984.  This is not necessarily horrible news, since it tends to be curable.

D.  However, months of jacking around has allowed lump to engulf some of the clavicles & sternum.  Involved area must be excised in an eight-hour operation, which goes well, taking only six hours.

E.  However, six weeks later, during the post-op iodine scan, it's found that the lump has regrown to it's pre-op size.

F.  The following week, we're told the x-ray was misread.  No lump at all.  My dad is doing great.  We're optimistic about a complete recovery.

In the middle of this, my best friend, a grad student in biochem who knew what he was doing, took cyanide.

Save your sympathy.  If I had any class, I wouldn't have mentioned this stuff at all and would have gotten Noesis out on time.  Thanks for letting me periodically try your patience.

Taking GRE's for credit is going well.  Taken four so far, plan on taking seven or eight more.  Any of you could accumulate years of college credit (one year per three-hour GRE!) doing the same thing.  Lemme know if you want to be bored with the specifics.

Just read that Ron Hoeflin is also increasing his dues to $2.00 an issue.  But here's my special deal to you, since it's taken so long to get these issues out.  Subscription money received between January 5 and February 10 will be credited at a cost of $1.60 an issue.  After that, it's two bucks per.  Please make checks payable to me, rather than to Noesis.  Thanks.

Daryl Inman recently had his analogy tests printed in two high-circulation magazines.  His Quest Test appears in this month's Omni (It's the new "World's Hardest I.Q. Test."), and his Crypto-Analogies Test appears in some Canadian mag called SBT.

Robert Hannon and Norman Hale--I've got material of yours to be stuck in the February issue.

SHORT FORM TEST
QUESTIONS AND ANSWERS TO DATE
WITH TWO NEW PROBLEMS

1.  Six squares can be joined edge-to-edge to form a two-dimensional shape.  Some of these shapes can be folded and joined along the squares' edges to form complete cubes.  How many different arrangements of six squares can be folded into cubes?  (Count reflections as distinct, but not rotations.) (Rick Rosner)

Answer: 20.

2. Eight cubes can be joined face-to-face to form a three-dimensional shape.  Some of these shapes can be folded and joined (fourth-dimensionally) along the cubes' faces to form hypercubes.  How many different arrangements of eight cubes can be folded to form hypercubes?  (Again, reflections, but not rotations, are distinct.) (Rick Rosner)

Hints:  I know the answer to the first problem, but the second is brutal.  You don't need to be able to think in 4D's to solve it, however.  Each member of the set of six-square shapes that can be folded into cubes may be transformed into any other member through a series of 90-degree rotations of its constituent squares around the squares' corners.  180-degree rotations are not allowed.

Similarly, each member of the set of eight-cube shapes that can be folded into tesseracts may be transformed into any other member through a series of 90-degree rotations of its constituent cubes around the cubes' edges.  Again, 180-degree rotations aren't kosher.  Any legal rotation produces a member of the set.  All you have to do is find one unfolded tesseract; the rest is just finding legal rotations in three dimensions.

There are as many ugly problems of this type as there are unfolded polyhedra and hyperpolyhedra.  The set of unfolded tetrahedra is trivial, and the set of unfolded octahedra is easy, (Is it equivalent to the set of unfolded cubes?  I forget.) as is the set of unfolded hypertetrahedra.  The sets of unfolded icosohedra and dodecahedra are nasty (but equivalent?).

Answer: ?

3.  0, 1 ,7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, 7, 7, 15, 15, 10, 23, 10, ?  (Eric Erlandson)

Answer: 111  (the number of operations of the famous "3x+1" function to work from n to 1)

4.  10, 10, 171, 186, 2748, 3258, 43981, 56506, 703710, 974010, 11259375, ?  (Eric Erlandson)

Answer: 16702650  (In hexadecimal, A, A, AB, BA, ABC, CBA, ABCD, DCBA, ABCDE, EDCBA, etc.)

5.  BODY : HOLE :: MAX : ?  (Mike Price)

Answer:  STEPHEN (black body radiation: black hole radiation :: Planck: Hawking)

6.  You are lost in a half-planar forest, bounded on one side by a linear road.  The forest is too dense for you to be able to see the road until you walk right up to it.  You know that you are within one mile of the road, but are unable to determine the direction to it.  What is the length of the shortest path that will guarantee your reaching the road?  (Dean Inada)

Answer:   miles

7.  If  what does  ?  (Chris Cole)

Answer:

8.  (Rick Rosner)

Answer:  a heptagon with concave sides and minus its middle.

9.  0, 20, 6, 2, 5, 4, 2, 6, 0, ?  (Jeffrey Wright)

Answer:  one quadrillion (smallest nonnegative integer containing each letter of the reverse alphabet)

10.  Consider the "volume" of an n-dimensional sphere of radius r.  For n=1, 2, 3 the "spheres" are the line segment, the circle, and the sphere, and the volumes are 2r, pr², and 4/3pr³.  What is the volume of an infinite-dimensional sphere, radius r?  (Marshall Fox)

Answer:  0  ()

11.  95 : 98 :: VENITE : ?  (Pomfrit)

Answer:   CANTATE

12.  MINCES : EYES :: PORKIES : ?  (Pomfrit)

Answer:   LIES

13.  2823 : 5331 :: ELEPHANT : ?  (Pomfrit)

Answer:   ANTIQUARIAN

14.  (Sharp)

Answer: ?

15.  At each point in the Cartesian plane whose coordinates are both integers, an equilateral triangle is centered.  Each triangle is free to pivot around its center, all triangles are the same size, and no triangles overlap.  What is the maximum length of the triangles' sides (and what is the maximum percentage of the plane's area they can cover)?  (Rosner)

Answer: ?

16.  A goat is tied to a post on the circumference of a circular meadow with a diameter of 100 meters.  Determine the goat's "radius of action" when the pasture ground within its reach is exactly one half of the circle's area.

Answer:  57.9365 square meters

17.  In what order are these signs arranged?

E      I      S      H      5

Answer:  Number of dots in Morse code.

18.  MORE : BOLSHEVIK :: LESS : ?  (Eric Erlandson)

19.  Given a solid sphere sliced by n planes,

    a.  Find a general expression for the maximum number of undivided volumes.

    b.  Calculate the number of these volumes which are tetrahedrons, pentahedrons, etc., and the number of volumes which have a section of the sphere surface as a "side."  Do the proportions of numbers of these various polyhedrons approach limits as n goes to infinity?  If so, calculate them.  (Glenn Morrison, extracted from letter later in this issue).

PROBLEM ANSWER

Dear Rick:

Here is my answer to problem 16, page 12, in Noesis 74, about the goat.  I get a radius of 57.936 meters.

Yours truly,

John W. Mathewson

[Right!  57.9365 gives you one more digit.]

ANALOGY PARIS
M.N. van der Riet
Republic of South Africa
October 1990

1. VICTORIANISM: HIPPOCRATISM :: VICTORIA:
2. VICTORIANISM: HIPPOCRATISM :: COINS:
3. NIGHT: DAY :: NOCTURNAL:
4. NIGHT: DAY :: NYCTALOPIA:
S. STABlLlSER: ELEVATOR :: FIN:
6. STABILISER: ELEVATOR :: WING:
7. GRAPE: PLUM :: VINEYARD:
8. GRAPE: PLUM :: BRANDY:
9. AMERICAN: RUSSIAN :: ASTRONAUT:
10. AMERICAN: RUSSIAN :: RUTHERFORDIUM:
11. MALE: FEMALE :: ARRHENOTOKY:
12. MALE: FEMALE :: DECATHLON:
13. TEA: COFFEE :: THEACEAE :
14. TEA: COFFEE :: INFUSION :
15. HUMAN: CATTLE :: CORPSE:
16. HUMAN : CATTLE :: EUNUCH:
17. FEMALE: MALE :: SIREN:
18. FEMALE: MALE :: CARYATID:
19. MOON : EARTH :: APOCYNTHION:
20. MOON: EARTH :: SELENIUM:
21. URSA MINOR: CANIS MAJOR :: BEAR:
22. URSA MINOR: CANIS MAJOR :: POLARIS:
23. GREENHEART: PROTOPLASM :: RENEGADE:
24. GREENHEART: PROTOPLASM :: GENERATE:
25. BILE: CHOLAGOGUE :: SMELL:
26. BILE: CHOLAGOGUE :: SALIVA:
27. JEW: CATHOLIC :: RABBINICAL:
28. JEW: CATHOLIC :: YARMULKE:
29. HYDROLYSIS: ESTERIFICATION :: EVAPORATION:
30. HYDROLYSIS: ESTERIFICATION :: K-CAPTURE:
31. ITALY : INDIA :: SICILY
32. ITALY: INDIA :: LATIN:
33. TRANSPARENT: DIAPHANOUS :: NEPTUNE:
34. TRANSPARENT: DIAPHANOUS :: ACUTIFOLIATE:
35. TOBACCO: NICOTINE :: CINCHONA:
36. TOBACCO: NICOTINE :: POMEGRANATE:
37. KIP: AT :: KYAT:
38. ICIP: AT :: LEU:
39. PIG: PORK :: GAME:
40. PIG: PORK :: SNAIL:
41. SECTIONAL: COASTLINE :: OOCYTE:
42. SECTIONAL: COASTLINE :: VACUOLATE:
43. BOL: ERO :: FLAM:
44. BOL: ERO :: LAB:
45. TREE: SPOON :: ARBOR:
46. TREE: SPOON :: BONG
47. PARIS: COPENHAGEN :: FRANCE:
48. PARIS: COPENHAGEN :: LUTETIUM:
49. RED: BLUE :: GREEN:
50. RED: BLUE :: ERYTHEMA:
51. 5169: 120 :: 1010000110001:
52. S169: 120 :: 1010111:
53. HEAT: WIND :: THERMOMETER:
54. HEAT: WIND :: IGNEOUS:
55. 5: 2 :: HE:
56. 5: 2 :: LOAF:
57. 2: 5 :: He:
58. 2: 5 :: DOMINO:
59. DOWN: UP :: SNAKE:
60. DOWN: UP :: STRANGE:
61. 4N + 3: 4N + 2 :: 7:
62. 4N + 3: 4N + 2 :: ACTINIUM:
63. FROLICSOME : MOORS :: STAGE-COACH:
64. FROLICSOME : MOORS :: SHIGELLA
65. CHILD: ADULT :: IMP:
66. CHILD: ADULT :: RACHITIS:
67. LOOK: TOUCH :: VISUAL:
68. LOOK: TOUCH :: VOYEUR:
69. ANAPAEST: DACTYL :: IAMBUS :
70. ANAPAEST: DACTYL :: U:
71. CRICK: WATSON :: PENZIAS:
72. CRICK: WATSON :: HERTZSPRUNG:
73. X: X + 1 :: HARVEST MOON:
74. X: X + 1 :: O H M S:
7S. HYDRA: HERCULES :: MEDUSA:
76. HYDRA: HERCULES :: CHIMAERA:
77. DISCRETE: CONTINUOUS :: CHILIAGON:
78. DISCRETE: CONTINUOUS :: BINOMIAL:
79. F#: G  :: STOAT:
80. F#: G  :: TERJUBILEE:
81. GENERAL: SPECIFIC :: GEOSYNCHRONOUS ORBIT:
82. GENERAL: SPECIFIC :: CRYPTARITHM:
83. 22: 9 :: LOLLO:
84. 22: 9 :: TITANIUM:
85. ARRIVAL: DEPARTURE :: LAND:
86. ARRIVAL: DEPARTURE :: RUDIMENT:
87. RUSSIA: SOMALIA :: MOSCOW:
88. RUSSIA: SOMALIA :: OBLAST:
89. IS: WAS :: ANTIMONY:
90. IS: WAS :: SCHIZOPHRENIA:
91. SiO2: TiO2 :: SILICON:
92. SiO2: TiO2 :: SILICA:
93. OHM : MHO :: SEMORDNILAP
94. OHM: MHO :: HALF:
95. AEEOUU: EUOUAE :: CHRTW:
96. AEEOUU: EUOUAE :: DKRTYZ:
97. MKS: MTS :: KILOGRAM:
98. MKS: MTS :: NEWTON:
99. APPLE: PEAR :: POMUM:
100. APPLE : PEAR :: CIDER:
101. RIDGE: FURROW :: GYRUS:
102. RIDGE: FURROW :: HORST:
103. 100: 9 :: MEDUSA: (INMAN)
104. 100: 9 :: PERCENTILE: (HOEFLIN)
105. CIS: TRANS :: MALEIC:
106. CIS: TRANS :: OLEIC:
107. 12: 21 :: 144:
108. 13: 31 :: 169:
109. 930: 969 :: CMXXX:
110. 930: 969 :: ADAM:
111. 2: 3 :: VENUS:
112. 2: 3 :: RELAPSE:
113. CONFESSION : OF SIN : CoNFeSSiON:
114. CONFESSION : OF SIN : GOBBLEDYGOOK:
115. SOLDIER : SAILOR :: MILES:
116. SOLDIER : SAILOR :: MILES PER HOUR:
117. VARICES : VISCERA :: VARIX:
118. VARICES : VISCERA :: ENTICER:
119. JOY: SORROW :: LAETITIA:
120. JOY: SORROW :: THALIA:

[If anyone doesn't want their name & number supplied, let me know.  Otherwise I'll send Mark Downey a list in February.--Ed.]

IN THE NEWS:
THE THREE CUBES

PRECIS FROM RICHARD W. MAY

ARTICLE FROM LEROY KOTTKE