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.
Palindromic numbers from around the interwebs.
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!
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