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3/9, 12/9 and 1/2 (Posted on 2009-06-30) Difficulty: 3 of 5
Solve each of these separate cryptarithms:
  • THREE/NINTHS = 3/9
     
  • TWELVE/NINTHS = 12/9
     
  • ONE/HALF = 1/2   (such that TWO+ONE+THREE = 32,213)

See The Solution Submitted by Dej Mar    
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Solution computer solution Comment 1 of 1
 three  ninths
 53844  161532
 
 twelve  ninths
 632812  474609
 
 one  half     one  two  three
 728  1456     728  397  31088
 
 


Without the "such that", the following would be solutions for ONE/HALF = 1/2:
 


 652  1304     852  1704     853  1706     654  1308     356  712
 456  912      358  716      458  916      359  718      413  826
 314  628      164  328      364  728      764  1528     865  1730
 416  832      267  534      218  436      219  438      269  538
 769  1538     523  1046     923  1846     273  546      176  352
 476  952      327  654      827  1654     927  1854     728  1456
 178  356      478  956      329  658      729  1458     179  358
 679  1358     431  862      381  762      481  962      532  1064
 932  1864     182  364      382  764      782  1564     134  268
 534  1068     635  1270     835  1670     935  1870     685  1370
 436  872      536  1072     936  1872     186  372      486  972
 138  276      238  476      538  1076     139  278      239  478
 539  1078     639  1278     341  682      391  782      192  384
 392  784      692  1384     792  1584     143  286      543  1086
 293  586      793  1586     645  1290     845  1690     546  1092
 148  296      548  1096
 

The cases of half showing as only three digits are instances where H is a leading zero.

CLS

FOR t = 0 TO 9
 used(t) = 1
FOR h = 0 TO 9
 IF used(h) = 0 THEN
  used(h) = 1
FOR r = 0 TO 9
 IF used(r) = 0 THEN
  used(r) = 1
FOR e = 0 TO 9
 IF used(e) = 0 THEN
  used(e) = 1
FOR n = 0 TO 9
 IF used(n) = 0 THEN
  used(n) = 1
FOR i = 0 TO 9
 IF used(i) = 0 THEN
  used(i) = 1
FOR s = 0 TO 9
 IF used(s) = 0 THEN
  used(s) = 1
 
three = t * 10000 + h * 1000 + r * 100 + e * 11
ninths = n * 101000 + i * 10000 + t * 100 + h * 10 + s
IF 9 * three / ninths = 3 THEN
   PRINT three; ninths
   REM
END IF

  used(s) = 0
 END IF
NEXT
  used(i) = 0
 END IF
NEXT
  used(n) = 0
 END IF
NEXT
  used(e) = 0
 END IF
NEXT
  used(r) = 0
 END IF
NEXT
  used(h) = 0
 END IF
NEXT
 used(t) = 0
NEXT


FOR t = 0 TO 9
 used(t) = 1
FOR w = 0 TO 9
 IF used(w) = 0 THEN
  used(w) = 1
FOR l = 0 TO 9
 IF used(l) = 0 THEN
  used(l) = 1
FOR e = 0 TO 9
 IF used(e) = 0 THEN
  used(e) = 1
FOR n = 0 TO 9
 IF used(n) = 0 THEN
  used(n) = 1
FOR i = 0 TO 9
 IF used(i) = 0 THEN
  used(i) = 1
FOR s = 0 TO 9
 IF used(s) = 0 THEN
  used(s) = 1
FOR v = 0 TO 9
 IF used(v) = 0 THEN
  used(v) = 1
FOR h = 0 TO 9
 IF used(h) = 0 THEN
  used(h) = 1
 
twelve = t * 100000 + w * 10000 + e * 1001 + l * 100 + v * 10
ninths = n * 101000 + i * 10000 + t * 100 + h * 10 + s
IF 9 * twelve / ninths = 12 THEN
 PRINT twelve; ninths
END IF

  used(h) = 0
 END IF
NEXT
  used(v) = 0
 END IF
NEXT
  used(s) = 0
 END IF
NEXT
  used(i) = 0
 END IF
NEXT
  used(n) = 0
 END IF
NEXT
  used(e) = 0
 END IF
NEXT
  used(l) = 0
 END IF
NEXT
  used(w) = 0
 END IF
NEXT
 used(t) = 0
NEXT

 

FOR t = 0 TO 9
 used(t) = 1
FOR w = 0 TO 9
 IF used(w) = 0 THEN
  used(w) = 1
FOR l = 0 TO 9
 IF used(l) = 0 THEN
  used(l) = 1
FOR e = 0 TO 9
 IF used(e) = 0 THEN
  used(e) = 1
FOR n = 0 TO 9
 IF used(n) = 0 THEN
  used(n) = 1
FOR o = 0 TO 9
 IF used(o) = 0 THEN
  used(o) = 1
FOR f = 0 TO 9
 IF used(f) = 0 THEN
  used(f) = 1
FOR a = 0 TO 9
 IF used(a) = 0 THEN
  used(a) = 1
FOR h = 0 TO 9
 IF used(h) = 0 THEN
  used(h) = 1
FOR r = 0 TO 9
 IF used(r) = 0 THEN
  used(r) = 1

one = o * 100 + n * 10 + e
half = h * 1000 + a * 100 + l * 10 + f
two = t * 100 + w * 10 + o
three = t * 10000 + h * 1000 + r * 100 + e * 11
IF 2 * one / half = 1 THEN
  IF one + two + three = 32213 THEN
    PRINT one; half, one; two; three
  END IF
END IF

  used(r) = 0
 END IF
NEXT
  used(h) = 0
 END IF
NEXT
  used(a) = 0
 END IF
NEXT
  used(f) = 0
 END IF
NEXT
  used(o) = 0
 END IF
NEXT
  used(n) = 0
 END IF
NEXT
  used(e) = 0
 END IF
NEXT
  used(l) = 0
 END IF
NEXT
  used(w) = 0
 END IF
NEXT
 used(t) = 0
NEXT


FOR l = 0 TO 9
 IF used(l) = 0 THEN
  used(l) = 1
FOR e = 0 TO 9
 IF used(e) = 0 THEN
  used(e) = 1
FOR n = 0 TO 9
 IF used(n) = 0 THEN
  used(n) = 1
FOR o = 0 TO 9
 IF used(o) = 0 THEN
  used(o) = 1
FOR f = 0 TO 9
 IF used(f) = 0 THEN
  used(f) = 1
FOR a = 0 TO 9
 IF used(a) = 0 THEN
  used(a) = 1
FOR h = 0 TO 9
 IF used(h) = 0 THEN
  used(h) = 1

one = o * 100 + n * 10 + e
half = h * 1000 + a * 100 + l * 10 + f
IF 2 * one / half = 1 THEN
    PRINT one; half,
END IF

  used(h) = 0
 END IF
NEXT
  used(a) = 0
 END IF
NEXT
  used(f) = 0
 END IF
NEXT
  used(o) = 0
 END IF
NEXT
  used(n) = 0
 END IF
NEXT
  used(e) = 0
 END IF
NEXT
  used(l) = 0
 END IF
NEXT

 


  Posted by Charlie on 2009-06-30 12:59:33
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