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

Only the middle of the following three solutions is valid as that is the only one in which U is even:

8  6  10      1  0  5  6    1  3  4  2
1044  1392  1740
1089936  1937664  3027600

9  5  8       1  4  6  5    1  7  2  10
1152  1886  2210
1327104  3556996  4884100

10  8  7      2  3  9  8    2  6  0  5
1305  3132  3393
1703025  9809424  11512449

So the alphametic is:

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

where A is the digit representing ten.

In decimal, that's 1152^2 + 1886^2 = 2210^2,
or 1327104 + 3556996 = 4884100.

DEFDBL A-Z

FOR t = 1 TO 10
used(t) = 1

FOR f = 1 TO 10
IF used(f) = 0 THEN
used(f) = 1

FOR r = 0 TO 10
IF used(r) = 0 THEN
used(r) = 1

FOR y = 0 TO 10
IF used(y) = 0 THEN
used(y) = 1
try = 121 * t + 11 * r + y
try2 = try * try

FOR o = 0 TO 10
IF used(o) = 0 THEN
used(o) = 1

FOR u = 0 TO 10
IF used(u) = 0 THEN
used(u) = 1
four = f * 1331 + o * 121 + u * 11 + r
four2 = four * four

FOR i = 0 TO 10
IF used(i) = 0 THEN
used(i) = 1

FOR v = 0 TO 10
IF used(v) = 0 THEN
used(v) = 1

FOR e = 0 TO 10
IF used(e) = 0 THEN
used(e) = 1
five = f * 1331 + i * 121 + v * 11 + e
five2 = five * five

IF five2 = try2 + four2 THEN
  PRINT t; r; y, f; o; u; r, f; i; v; e
  PRINT try; four; five
  PRINT try2; four2; five2
  PRINT
END IF

used(e) = 0
END IF
NEXT

used(v) = 0
END IF
NEXT

used(i) = 0
END IF
NEXT

used(u) = 0
END IF
NEXT

used(o) = 0
END IF
NEXT

used(y) = 0
END IF
NEXT

used(r) = 0
END IF
NEXT

used(f) = 0
END IF
NEXT

used(t) = 0
NEXT

 

Posted by Charlie on 2009-05-27 13:04:44