Problem 11. Palindrome Numbers
What is the 12345’th positive number that is palindrome (equal to its reverse)? The first positive palindrome number is 1.
Link to the problem on Twitter: https://twitter.com/Riazi_Cafe/status/1676156294665850880
. The answer is equal to 23466432.
According to the table below, because the 12345’th palindrome number is placed between the 10999’th and 19999’th palindrome numbers, it has 8 digits. More precisely, the answer to this question is the 1346’th palindrome number with 8 digits.
| index of the first palindrome number | number of digits | number of palindrome numbers |
|---|---|---|
| 1 | 1 | 9 |
| 10 | 2 | 9 |
| 19 | 3 | 90 |
| 109 | 4 | 900 |
| 1999 | 5 | 900 |
| 1099 | 6 | 9000 |
| 999 | 7 | 9000 |
| 10999 | 8 | 9000 |
| 1999 | 9 | 90000 |
Since the first palindrome number with 8 digits is equal to 10000001, then the 1346’th palindrome number with 8-digits is equal to 23466432.
Link to the solution on Twitter: https://twitter.com/Riazi_Cafe/status/1676794374548598784