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 Different Digits (Posted on 2003-12-28)
Different letters represent different numbers and none of them is equal to zero.

```  NOSIER
+ ASTRAL
725613```
What word does the final result represent ?

 See The Solution Submitted by Ravi Raja Rating: 3.2857 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Solution | Comment 2 of 14 |
(In reply to Solution by e.g.)

I agree there are probably more elegant methods, but even with an inelegant method, a solution is more than just the answer. Here's my solution in the form of a program, which had taken me more time to write than the 8 minutes e.g. took.

DECLARE SUB permute (a\$)
CLS
a1\$ = "nosier"
a2\$ = "astral"
tr\$ = "nosieratl"
FOR perm = 1 TO 362880
v1\$ = a1\$
FOR i = 1 TO LEN(v1\$)
MID\$(v1\$, i, 1) = LTRIM\$(STR\$(INSTR(tr\$, MID\$(v1\$, i, 1))))
NEXT
v2\$ = a2\$
FOR i = 1 TO LEN(v2\$)
MID\$(v2\$, i, 1) = LTRIM\$(STR\$(INSTR(tr\$, MID\$(v2\$, i, 1))))
NEXT
t = VAL(v1\$) + VAL(v2\$)
IF t = 725613 THEN
PRINT "123456789"
PRINT tr\$
s1\$ = ""
FOR i = 1 TO LEN("725613")
s1\$ = s1\$ + MID\$(tr\$, VAL(MID\$("725613", i, 1)), 1)
NEXT
PRINT s1\$
PRINT
END IF
permute tr\$
NEXT

SUB permute (a\$)
DEFINT A-Z
x\$ = ""
FOR i = LEN(a\$) TO 1 STEP -1
l\$ = x\$
x\$ = MID\$(a\$, i, 1)
IF x\$ < l\$ THEN EXIT FOR
NEXT

IF i = 0 THEN
FOR j = 1 TO LEN(a\$) \ 2
x\$ = MID\$(a\$, j, 1)
MID\$(a\$, j, 1) = MID\$(a\$, LEN(a\$) - j + 1, 1)
MID\$(a\$, LEN(a\$) - j + 1, 1) = x\$
NEXT
ELSE
FOR j = LEN(a\$) TO i + 1 STEP -1
IF MID\$(a\$, j, 1) > x\$ THEN EXIT FOR
NEXT
MID\$(a\$, i, 1) = MID\$(a\$, j, 1)
MID\$(a\$, j, 1) = x\$
FOR j = 1 TO (LEN(a\$) - i) \ 2
x\$ = MID\$(a\$, i + j, 1)
MID\$(a\$, i + j, 1) = MID\$(a\$, LEN(a\$) - j + 1, 1)
MID\$(a\$, LEN(a\$) - j + 1, 1) = x\$
NEXT
END IF
END SUB

It found

```
123456789

tnsaleiro

inlets

```

-----
the first two lines being the full number-to-letter encoding.
Edited on December 28, 2003, 10:16 am
 Posted by Charlie on 2003-12-28 10:15:20

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