A palindrome is a number that reads the same forward and backward, such as 242.
A palindrome is a number that reads the same forward and backward, such as 242. How many even eleven-digit numbers are palindromes?
Answer/Solution
400,000
Steps/Work
if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.
The middle number in the eleven-digit could be 0-9 ( 10 ways), e.g 22522, 22822
The 2nd and fourth numbers , 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)
we thus have, 4 *10*10*10*10*10* = 400000. E
The middle number in the eleven-digit could be 0-9 ( 10 ways), e.g 22522, 22822
The 2nd and fourth numbers , 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)
we thus have, 4 *10*10*10*10*10* = 400000. E