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 Numerology (Posted on 2009-02-28)
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 No Rating

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 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 microspectrophotometerindistinguishablenesses 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 16910  41 181     10  66 171     10  64 16911  59 197     11  55 190     11  64 19612  71 199     12  91 210     12  81 19613  73 211     13 105 210     13 100 19614 103 241     14 120 210     14 121 22515 113 241     15 136 231     15 144 22516 131 263     16 153 231     16 144 22517 149 257     17 153 253     17 169 25618 151 281     18 190 253     18 169 25619 179 281     19 210 253     19 225 25620 197 277     20 190 276     20 196 25621 211 281     21 231 276     21 289 28922 239 307     22 276 300     22 289 28923 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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