Solve this alphametic, where each of the capital letters in bold denotes a different base 11 digit from 0 to A. None of the numbers contains a leading zero and U is even.

(TRY)² + (FOUR)² = (FIVE)²

I found the following 2 solutions

792^2+ 3069^2= 3158^2

958^2+ 1465^2= 172A^2

using the following code

CLS 0
DIM digits(0 TO 10) AS STRING
FOR i = 0 TO 9
digits(i) = STR$(i)
NEXT i
digits(10) = "A"
FOR t = 1 TO 10
 FOR r = 0 TO 10
  IF r <> t THEN
   FOR y = 0 TO 10
    IF y <> t AND y <> t THEN
     v1 = y + 11 * r + (11 ^ 2) * t
     v1 = v1 ^ 2
     FOR f = 1 TO 10
      IF f <> t AND f <> r AND f <> y THEN
       FOR o = 0 TO 10
        IF o <> t AND o <> r AND o <> y AND o <> f THEN
         FOR u = 2 TO 10 STEP 2
          IF u <> t AND u <> r AND u <> y AND u <> f AND u <> o THEN
           v2 = r + 11 * u + (11 ^ 2) * o + (11 ^ 3) * f
           v2 = v2 ^ 2
           FOR i = 0 TO 10
            IF i <> t AND i <> r AND i <> y AND i <> f AND i <> o AND i <> u THEN
             FOR v = 0 TO 10
              IF v <> t AND v <> r AND v <> y AND v <> f AND v <> o AND v <> u AND v <> i THEN
               FOR e = 0 TO 10
                IF e <> t AND e <> r AND e <> y AND e <> f AND e <> o AND e <> u AND e <> i AND e <> v THEN
                 v3 = e + 11 * v + (11 ^ 2) * i + (11 ^ 3) * f
                 v3 = v3 ^ 2
                 IF v1 + v2 = v3 THEN
                  dsp$ = digits(t) + digits(r) + digits(y) + "^2+" + digits(f) + digits(o) + digits(u) + digits(r) + "^2="
                  dsp$ = dsp$ + digits(f) + digits(i) + digits(v) + digits(e) + "^2"
                  PRINT dsp$
                 END IF
                END IF
               NEXT e
              END IF
             NEXT v
            END IF
           NEXT i
          END IF
         NEXT u
        END IF
       NEXT o
      END IF
     NEXT f
    END IF
   NEXT y
  END IF
 NEXT r
NEXT t

 

Posted by Daniel on 2009-05-27 11:58:08