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 A palindrome product (Posted on 2012-09-05)
Find the largest palindrome which is a product of two 3-digit numbers.

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 computer solution | Comment 2 of 4 |

CLS
FOR a = 100 TO 999
FOR b = a TO 999
prod = a * b
p\$ = LTRIM\$(STR\$(prod))
pal = 1
FOR i = 1 TO LEN(p\$) / 2
IF MID\$(p\$, i, 1) <> MID\$(p\$, LEN(p\$) + 1 - i, 1) THEN pal = 0: EXIT FOR
NEXT
IF pal THEN
IF ct = 0 THEN PRINT a, b, prod
ct = ct + 1
IF prod >= prodmax THEN
asav = a: bsav = b: psav = prod
prodmax = prod
END IF
END IF
NEXT
NEXT
PRINT asav, bsav, psav
PRINT ct

PRINT

FOR a = 100 TO 999
FOR b = 100 TO 999
prod = a * b
p\$ = LTRIM\$(STR\$(prod))
pal = 1
FOR i = 1 TO LEN(p\$) / 2
IF MID\$(p\$, i, 1) <> MID\$(p\$, LEN(p\$) + 1 - i, 1) THEN pal = 0: EXIT FOR
NEXT
IF pal THEN
IF prod = prodmax THEN
PRINT a, b, prod
END IF
END IF
NEXT
NEXT

101           101           10201
913           993           906609
1239

913           993           906609
993           913           906609

indicating the lowest is 101*101=10201 and the highest product is 913*993=906609 and there are 1239 products of two 3-digit integers with palindromic products, not counting reversals. The only way to achieve 906609 by multiplying 3-digit numbers is by 913*993 as 906609=3*11*83*331.

 Posted by Charlie on 2012-09-05 12:58:56

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