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 3/9, 12/9 and 1/2 (Posted on 2009-06-30)
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 No Rating

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 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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