Find a base ten perfect square of 12 digits formed from the concatenation of
two base ten perfect squares, one having 4 digits and the other 8 digits. None of the three perfect squares can begin with a zero.
1024  57608100 = 102457608100
1521  97515625 = 152197515625
2401  98010000 = 240198010000
3249  57002500 = 324957002500
3844  24800400 = 384424800400
3969  25200400 = 396925200400
6241  77422401 = 624177422401
8649  55800900 = 864955800900
9801  99002500 = 980199002500
None were found with the 8digit square concatenated before the 4digit square.
Perhaps the "best" one is 152197515625, as it not only has no leading zeros, but no zeros at all.
DEFDBL AZ
a0 = INT(SQR(1000)): a1 = INT(SQR(9999))
b0 = INT(SQR(10000000)): b1 = INT(SQR(99999999))
CLS
FOR a = a0 TO a1
asq = a * a
FOR b = b0 TO b1
bsq = b * b
ck1 = 100000000 * asq + bsq
ck2 = 10000 * bsq + asq
sr1 = INT(SQR(ck1) + .5)
sr2 = INT(SQR(ck2) + .5)
IF sr1 * sr1 = ck1 THEN PRINT ck1
IF sr2 * sr2 = ck2 THEN PRINT " "; ck2
NEXT
NEXT

Posted by Charlie
on 20110925 16:24:27 