For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 <> 5 + 6

Let t = tens digit and o = ones digit

P(n) = to

S(n) = t + o

P(n) + S(n) = to + t + o

N = 10t + o

Set them equal to each other N = P(N) + S(N)

10t + o = to + t + o

o's cancel, so we have

10t = to + t

Subtract t from each side, we have

9t = to

Divide each side by t

o = 9

So any two-digit number with 9 as the ones digit will work:

**{19,29,39,49,59,69,79,89,99}**