Palindrome vs Level of Palindrome The palindrome, example: $131$, $82728$, $55655$. But from the palindrome maker algorithm say: If $17$ isn't palindrome you must additive by reverse of them $33$ is say $P(1)$ palindrome $38$ is say $P(2)$ semipalindrome of level $1$ Because: $38+83=121$ $182$ is say $P(5)$ semipalindrome of level $4$ Because: $182+281=463$ $463+364=827$ $827+728=1555$ $1555+5551=6666$ > So the question is: > > How many semipalindrome of level $1$ between $1-1000$ are?

If you start with a two digit number $ab$ you get a palindrome in two cases:

* if $a+b \lt 10$ there will be no carry so you get $11(a+b)$

* if you carry $1$ and the ones digit is $1$, so when $a+b=11$




If you start with a three digit number $abc$ you get a palindrome:

* if there are no carries at all
* if $a+c =11$ so the ones digit of the sum is $1$ and there is a carry, then $2b+1$ does not carry and matches the $1$ that $a+c$ gives in the hundreds, so $b=0$
* if $a+c=11$ and $2b+1$ does carry there will be a $2$ in the hundreds, which $2b+1$ cannot match. This does not work.