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!