Many numbers can be expressed as the sum of two palindromes. 389 for instance is 383 + 6 as well as 323 + 66.
What three-digit number cannot be expressed as the sum of two palindromes?
(For the sake of this problem, palindromes with leading zeroes [like 030 and 0550] are not allowed, and neither are negative numbers or non-integers. Single digits are allowed.)
Tags: puzzle
111, 131, 141, 151, 161, 171, 181, 191, 201
I may have cheated because I did it programmatically with PHP :P
1) Made an array of all the palindromes under 1000 (1…9, 11…99, 101…999)
2) Made an array of all the sums of these palindromes
3) Made an array of all the numbers from 100 to 999 which are not in the array from step 2
I just realized I could have folded steps 1 and 2 together, but ehh, processor cycles (and RAM) are cheap :D
The first eight of those ARE palindromes. XD I wasn’t clear in the instructions, but technically those can be expressed as the sum of one palindrome, themselves.
201 is it though. high five!
Well then you should have specified a non-palindrome (palindromic?) three-digit number :P
I did think it was a strange coincidence that palindromes showed up in the list. Did you make this puzzle yourself? If so, how did you notice this pattern? :D
I have no life. XD