Question 756857
{{{N=10t+u}}}
{{{t}}} = tens digit of {{{N}}}
{{{u}}} = units digit of {{{N}}}
{{{T+u}}} = sum of digits of {{{N}}}
 
{{{N+2=10t+u+2}}}
 
If {{{u+2<10}}}, then
{{{u+2}}} is the units digit of {{{N+2=10t+u+2}}},
{{{t}}} is the tens digit of {{{N+2}}},
{{{t+u+2>t+u}}} is the sum of digits of {{{N+2}}},
and {{{N}}} is not a solution.
 
If {{{u+2>=10}}} <--> {{{highlight(u>=8)}}}, then
the units digit of {{{N+2=10t+u+2=10(t+1)+u+2-10}}} is
{{{u+2-10=u-8}}}, and
{{{t+1}}} is the tens digit of {{{N+2}}}.
Then, the sum of digits of {{{N+2}}} is
and {{{N}}} is a solution.
All numbers ending in 8 or 9 are solutions.
 
Examples of solutions for N: 18, 19, 28, 29, 38, 39, ...
N=18, sum of digits of 18=9, N+2=20, sum of digits of N+2 = 2
N=19, sum of digits of 19=10, N+2=21, sum of digits of N+2 = 3
N=28, sum of digits of 28=10, N+2=30, sum of digits of N+2 = 3
N=29, sum of digits of 29=11, N+2=31, sum of digits of N+2 = 4