In this alphametic equation, each of the capital letters in bold denotes a different base ten digit from 0 to 9, and x is any positive integer ≤ 16. None of R and T can be zero.

REKNIT        9*x
---------- = -----------
TINKER      9*x + 1

Determine the minimum value of REKNIT and maximum value of TINKER.

I concur with Daniel's solution but we have approached the programming differently, and I have used QuickBasic and one of Charlie's 'formats'; and I have indicated the 'x' values. 

TINKER  REKNIT  x   Ratio of RHS
 208791  197802   2  .9473684    Min REKNIT
 307692  296703   3  .9642857  
 406593  395604   4  .972973  
 604395  593406   6  .9818182  
 703296  692307   7  .984375   
 802197  791208   8  .9863014    Max REKNIT

CLS

OPEN "tinker.txt" FOR OUTPUT AS #1
DIM SHARED used(10)

FOR r = 1 TO 9
IF used(r) = 0 THEN
used(r) = 1
FOR e = 0 TO 9
IF used(e) = 0 THEN
used(e) = 1
FOR k = 0 TO 9
IF used(k) = 0 THEN
used(k) = 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 t = r + 1 TO 9
IF used(t) = 0 THEN
used(t) = 1

tinker = 10 ^ 5 * t + 10 ^ 4 * i + 10 ^ 3 * n + 10 ^ 2 * k + 10 * e + r
reknit = 10 ^ 5 * r + 10 ^ 4 * e + 10 ^ 3 * k + 10 ^ 2 * n + 10 * i + t

rat1 = reknit / tinker

FOR x = 1 TO 16
rat2 = (9 * x) / (9 * x + 1)

IF rat1 = rat2 THEN
PRINT #1, tinker; reknit; x; rat1; rat2
PRINT tinker; reknit; x; rat1; rat2
END IF
NEXT x

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

CLOSE 1

Posted by brianjn on 2009-10-05 03:52:38