In this alphametic equation, each of the small letters in bold denotes a different base b digit from 0 to b-1. Neither t nor n can be zero.

(ten)*(ten) - ten = ninety

Determine the minimum value of b, for which there exists at least one solution to the above equation.

DEFDBL A-Z
DIM used(100)
FOR b = 5 TO 100
 FOR t = 1 TO b - 1
  IF used(t) = 0 THEN
    used(t) = 1
 FOR n = 1 TO b - 1
  IF used(n) = 0 THEN
    used(n) = 1
 FOR e = 0 TO b - 1
  IF used(e) = 0 THEN
    used(e) = 1
 FOR i = 0 TO b - 1
  IF used(i) = 0 THEN
    used(i) = 1
 FOR y = 0 TO b - 1
  IF used(y) = 0 THEN
    used(y) = 1
  
    ten = t * b * b + e * b + n
    ninety = y + b * (t + b * (e + b * (n + b * (i + b * (n)))))
    IF ten * ten - ten = ninety THEN
      PRINT b, t; e; n, n; i; n; e; t; y, ten; ninety
    END IF
  
    used(y) = 0
  END IF
 NEXT
    used(i) = 0
  END IF
 NEXT
    used(e) = 0
  END IF
 NEXT
    used(n) = 0
  END IF
 NEXT
    used(t) = 0
  END IF
 NEXT
NEXT

to get

11            6  7  4       4  0  4  7  6  1            807  650442

for the base, the numbers ten and ninety, and those values in decimal.

Posted by Charlie on 2009-10-25 13:44:22