Problem 4

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99.

Find the largest palindrome made from the product of two 3-digit numbers.

Solution

–A palindromic number reads the same both ways.

–The largest palindrome made from the product of

–two 2-digit numbers is 9009 = 91  99.

 

–Find the largest palindrome made from the

–product of two 3-digit numbers.

 

— this is a fun query

— we join the number table to

— itself ensuring that the right

— number is greater than or equal

— to the left number

SELECT MAX(LeftNumber.number * RightNumber.number)

FROM Number LeftNumber

INNER JOIN Number RightNumber

ON LeftNumber.number <= RightNumber.number

— then we limit the numbers to 3 digits

— an obvious (and better) method for this is

— LeftNumber.number >= 100

— and LeftNumber.number <= 999

— but this technique is more interesting

WHERE LEN(CAST(LeftNumber.number AS VARCHAR)) = 3

and LEN(CAST(RightNumber.number AS VARCHAR)) = 3

— finally, the clever part is determining

— the palindromicity of the product

and(CAST(LeftNumber.number * RightNumber.number AS VARCHAR)

  = REVERSE(CAST(LeftNumber.number * RightNumber.number AS VARCHAR)))

 

Discussion

I am quite happy with this solution.

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).