# GeekDad Puzzle of the Week Solution – Palindromic Products

This week’s puzzle, as previously posted:

The smallest three-digit palindromic product of two, two-digits numbers happens to be a perfect square: 11 x 11 = 121. The largest three-digit palindromic product of two, two-digits numbers is 999 = 37 x 27, and the smallest four-digit palindromic product of two, two-digit numbers is 1001 = 91 x 11. The largest four-digit palindromic product of two, two-digit numbers? 91 x 99 = 9009.

This week’s Geekdad Puzzle of the Week is straightforward: What are the largest and smallest palindromic products of the appropriate set of digit-sizes for each of three, four, and five-digit numbers? Note that like two-digits numbers, above, there may be more than one digit-size applicable.

Congratulations to Blaine for submitting one of the many correct answers to this week’s puzzle. The coveted \$50 ThinkGeek Gift Certificate for this week will bear his favored name!

Here is the list of multiplicands and products that fill out each digit combination possible.

Multiplicand Digits Multiplicands Palindromic
Product
Product Digits
2 11 x 11 121 3
27 x 37 999
13 x 77 1001 4
91 x 99 9009
3 101 x 101 10201 5
271 x 369 99999
143 x 707 101101 6
913 x 993 906609
4 1001 x 1001 1002001 7
2151 x 4649 9999999
1781 x 5621 10011001 8
1507 x 6643 10011001
9901 x 9999 99000099
5 10001 x 10001 100020001 9
16667 x 59997 999969999
19999 x 50001 999969999
19019 x 52579 1000000001 10
99681 x 99979 9966006699

Thanks to everyone that reads and participates with these puzzles. Happy puzzling!