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Numerology (Posted on 2009-02-28) Difficulty: 4 of 5
Assign the values of 1 through 26 respectively to A through Z.

Find words of x letters (all letters and words1 different) such that the sum of letter values becomes the word value that fits each table category.

The table values represent the best values, being the lowest and highest, for which I was able; the left column represents word length. Can you also do better by providing a word lower or higher than the table value?

The blank cells are for those who wish to press this further.

Prime

Triangle

Square

Lowest

Highest

Lowest

Highest

Lowest

Highest

3

7

61

6

66

9

64

4

13

79

15

78

16

64

5

19

89

21

91

36

81

6

37

109

36

91

49

100

7

47

97

66

78

81

100

8

9

1Special note: Should a word score 36 (being both a triangle and square) neither a repetition of it nor any anagrams is considered acceptable.

See The Solution Submitted by brianjn    
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Solution computer solution | Comment 1 of 10

DECLARE FUNCTION numVal! (w$)
DIM lowPrime$(3 TO 26), highPrime$(3 TO 26)
DIM lowTriangle$(3 TO 26), highTriangle$(3 TO 26)
DIM lowSquare$(3 TO 26), highSquare$(3 TO 26)
DIM lowP(3 TO 26), highP(3 TO 26)
DIM lowT(3 TO 26), highT(3 TO 26)
DIM lowS(3 TO 26), highS(3 TO 26)

FOR i = 3 TO 26
  lowP(i) = 99999
  lowT(i) = 99999
  lowS(i) = 99999
NEXT

OPEN "wordswords.txt" FOR INPUT AS #1

DO
 LINE INPUT #1, w$
 w$ = LTRIM$(RTRIM$(w$))
 IF LCASE$(w$) = w$ AND LEN(w$) > 2 THEN
  v = numVal(w$): l = LEN(w$)
  IF l = 3 AND v = 64 THEN PRINT w$
   ' above line to find alternative to oxy
  isPrime = 0: isTri = 0: isSqu = 0
  OPEN "primes.txt" FOR INPUT AS #10
  DO
   INPUT #10, pr
   IF v = pr THEN isPrime = 1: EXIT DO
  LOOP UNTIL EOF(10) OR pr > v
  CLOSE 10
 
  sr = INT(SQR(1 + 8 * v) + .5)
  IF sr * sr = 1 + 8 * v THEN isTri = 1
 
  sr = INT(SQR(v) + .5)
  IF sr * sr = v THEN isSqu = 1

  IF isPrime THEN
   IF v < lowP(l) THEN lowP(l) = v: lowPrime$(l) = w$
   IF v > highP(l) THEN highP(l) = v: highPrime$(l) = w$
  END IF
  IF isTri THEN
   IF v < lowT(l) THEN lowT(l) = v: lowTriangle$(l) = w$
   IF v > highT(l) THEN highT(l) = v: highTriangle$(l) = w$
  END IF
  IF isSqu THEN
   IF v < lowS(l) THEN lowS(l) = v: lowSquare$(l) = w$
   IF v > highS(l) THEN highS(l) = v: highSquare$(l) = w$
  END IF
 END IF
LOOP UNTIL EOF(1)
CLOSE 1
FOR i = 3 TO 26
 IF lowP(i) < 99999 OR highP(i) > 2 OR lowT(i) < 99999 OR highT(i) > 2 OR lowS(i) < 99999 OR highS(i) > 2 THEN
   PRINT USING "####"; i; lowP(i); highP(i); : PRINT "   ";
   PRINT USING "####"; i; lowT(i); highT(i); : PRINT "   ";
   PRINT USING "####"; i; lowS(i); highS(i); : PRINT "   ";
 END IF
 PRINT
NEXT

OPEN "numerlgy.txt" FOR OUTPUT AS #2
FOR i = 3 TO 26
 IF lowP(i) < 99999 OR highP(i) > 2 OR lowT(i) < 99999 OR highT(i) > 2 OR lowS(i) < 99999 OR highS(i) > 2 THEN
   IF lowPrime$(i) > "" THEN PRINT #2, lowPrime$(i); " "; :  ELSE PRINT #2, " . ";
   IF highPrime$(i) > "" THEN PRINT #2, highPrime$(i); "    "; :  ELSE PRINT #2, " .    ";
   IF lowTriangle$(i) > "" THEN PRINT #2, lowTriangle$(i); " "; :  ELSE PRINT #2, " . ";
   IF highTriangle$(i) > "" THEN PRINT #2, highTriangle$(i); "    "; :  ELSE PRINT #2, " .    ";
   IF lowSquare$(i) > "" THEN PRINT #2, lowSquare$(i); " "; :  ELSE PRINT #2, " . ";
   IF highSquare$(i) > "" THEN PRINT #2, highSquare$(i); "    "; :  ELSE PRINT #2, " .    ";
   PRINT #2,
 END IF
NEXT

END

FUNCTION numVal (w$)
  t = 0
  FOR i = 1 TO LEN(w$)
   t = t + INSTR("abcdefghijklmnopqrstuvwxyz", MID$(w$, i, 1))
  NEXT
  numVal = t
END FUNCTION

 

 

bad tut    cab wry    aba oxy    
aced putz    abba onyx    alba oozy   
baaed wussy    bacca fusty    abaci nutty   
cabbed syzygy    baccae scuzzy    abided luxury   
addable zyzzyva    cabbage bowwows    acceded extorts   
academia quixotry    abapical surtouts    cabbaged outports   
beachhead torturous    bacchanal susurrous    abdicated outstunts   
deadheaded outthrusts    accidences outsprints    bacchanals mutinously   
deacidified luxuriously    bacchanalia myxoviruses    backpedaled murmurously   
abracadabras prosperously    amphibrachic prostitutors    decalcomania prostitution   
dieffenbachia expostulatory    beneficiaries southwesterly    adiabatically counterstyles   
bibliomaniacal presumptuously    boneheadedness contortionists    cleanabilities overscrupulous   
mechanochemical luxuriousnesses    affordabilities constructivists   
                                                                accessibilities supersymmetries   
deacidifications voluptuousnesses    accidentalnesses counterterrorism   
                                                                boneheadednesses anthropomorphist   
ineradicabilities counterterrorists    exchangeabilities immunosuppressant   
                                                                bacteriologically illustriousnesses   
biodegradabilities unscrupulousnesses    establishmentarian counterstrategists   
                                                                disagreeablenesses expressionlessness   
angiocardiographies structurelessnesses    comprehensibilities diethylstilbestrols   
                                                                circumstantialities dimethyltryptamines   
radiopharmaceuticals counterdemonstrators    electrocardiographic immunohistochemistry   
                                                                electroencephalogram countersurveillances   
electrocardiographies undemonstrativenesses    establishmentarianism immunocytochemistries   
                                                                unconstitutionalities unconstitutionalities   
encephalomyocarditises otorhinolaryngologists    nonrepresentationalism reinstitutionalization   
                                                                microspectrophotometer microspectrophotometer
indistinguishablenesses hexamethylenetetramines     .  .     .  .   
dichlorodifluoromethanes microspectrophotometries    intercomprehensibilities intercomprehensibilities     .  .   

 

An added line from the program shows an alternate for oxy is sty, as oxy is really only a prefix.

 

The stats are:

 

 3   7  61      3   6  66      3   4  64
 4  13  83      4   6  78      4  16  81
 5  13 107      5  10  91      5  16 100
 6  17 127      6  15 120      6  25 121
 7  29 151      7  21 120      7  25 121
 8  37 149      8  45 153      8  25 144
 9  37 167      9  45 171      9  49 169
10  41 181     10  66 171     10  64 169
11  59 197     11  55 190     11  64 196
12  71 199     12  91 210     12  81 196
13  73 211     13 105 210     13 100 196
14 103 241     14 120 210     14 121 225
15 113 241     15 136 231     15 144 225
16 131 263     16 153 231     16 144 225
17 149 257     17 153 253     17 169 256
18 151 281     18 190 253     18 169 256
19 179 281     19 210 253     19 225 256
20 197 277     20 190 276     20 196 256
21 211 281     21 231 276     21 289 289
22 239 307     22 276 300     22 289 289
23 263 269     23 --- ---     23 --- --- 
24 269 317     24 276 276     24 --- ---

Edited on February 28, 2009, 3:53 pm

Edited on February 28, 2009, 3:56 pm
  Posted by Charlie on 2009-02-28 15:52:40

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