Pretty Puzzling Palindrome Problem
Number Theory
Level
pending
A palindrome is a number which the same forwards and backwards, like 1991. What is the 2017th smallest positive integer palindrome?
The answer is 1018101.
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1 solution
The first and last digit cannot be 0 so there are 9 options for this. However, every other pair of digits has 10 options. For up to 6 digits there are 9+9+9×10+9×10+9×10×10+9×10×10=1998 numbers. So, we find the 2017-1998=19th 7 digit palindrome to be 1018101.