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 Nostra culpa (Posted on 2010-09-03)
WE + ARE +VERY = SORRY
For what value(s) of Y there is only one solution?

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 Two Means | Comment 4 of 5 |
I have been "advised" that the program listing below tells me something that it doesn't.

The program merely determines a set of values which are consistent with the expression.  It does not attempt to determine uniqueness.  The 'error' in my comment, now rectified, was due to incorrectly interpreting the problem text.

Using pencil and paper I derived Y=3 or 4, as in the these algorithms:

we        75
are      625
very    9523
sorry  10223

we        75
are      625
very    9524
sorry  10224

To confirm that they were the only solutions I wrote a program which gave both of the above as well as those below:

we        65
are      735
very    9532
sorry  10332

we        65
are      735
very    9534
sorry  10334

we        65
are       735
very    9538
sorry  10338

we        75
are       625
very    9528
sorry  10228

The program yields y = {2,3,4,8}  but when y=2 or y=3 there is only one result for each.

The program listing:

CLS
OPEN "sorry.txt" FOR OUTPUT AS #1

FOR w = 1 TO 9
IF used(w) = 0 THEN
used(w) = 1
FOR e = 0 TO 9
IF used(e) = 0 THEN
used(e) = 1
FOR a = 1 TO 9
IF used(a) = 0 THEN
used(a) = 1
FOR r = 0 TO 9
IF used(r) = 0 THEN
used(r) = 1
FOR v = 1 TO 9
IF used(v) = 0 THEN
used(v) = 1
FOR y = 0 TO 9
IF used(y) = 0 THEN
used(y) = 1
FOR s = 1 TO 9
IF used(s) = 0 THEN
used(s) = 1
FOR o = 0 TO 9
IF used(o) = 0 THEN
used(o) = 1

we = w * 10 + e
are = a * 100 + r * 10 + e
very = v * 1000 + e * 100 + r * 10 + y
sorry = s * 10000 + o * 1000 + r * 100 + r * 10 + y
IF (sorry = we + are + very) THEN
PRINT "   we    "; we
PRINT "  are   "; are
PRINT " very  "; very
PRINT "sorry "; sorry
PRINT
PRINT #1, "   we    "; we
PRINT #1, "  are   "; are
PRINT #1, " very  "; very
PRINT #1, "sorry "; sorry
PRINT #1,
END IF

used(o) = 0
END IF
NEXT

used(s) = 0
END IF
NEXT

used(y) = 0
END IF
NEXT

used(v) = 0
END IF
NEXT

used(r) = 0
END IF
NEXT

used(a) = 0
END IF
NEXT

used(e) = 0
END IF
NEXT

used(w) = 0
END IF
NEXT

CLOSE 1

Edited on September 13, 2010, 9:26 pm
 Posted by brianjn on 2010-09-04 05:34:25

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