Number puzzle #67, 4+5+4+5=81

First lets understand the pattern
4+5+4+5 => 18 => 1+8 => 9 => square of 9 => 81
5+6+5+6 => 22 => 2+2 => 4 => square of 4 => 16
6+7+6+7 => 26 => 2+6 => 8 => square of 8 => 64

Thus the patter is sum of the digits till we get single digit and then square of the the single digit.

Method 1:
So lets assume the missing number is x

thus 1+2+1+x = x + 4
Now if x is less then or equal to 5(i.e. x+4 is single digit)
(x+4)(x+4) = 16 => x = 0

Now if x is greater then 5( i.e. x + 4 is two digit number)
lets replace x by 6+y (where y is single digit)

x+4 => 6+y+4 => 10 + y => y +1 => (y+1)*(y+1) = 16 => y = 3

thus x = 6+y = 9.

Note: If we assume missing number can be more then single digit.

Method 2:

its the reverse engineering method => to get 16 the sum of digits should be 4

we already have 1+2+1 = 4 thus missing number can be 0
other ways to get the sum of digits as 4 => 13, i.e. missing number = 13-4 = 9
other ways is 22, i.e. missing number 22-4 = 18
other way is 31, i.e. missing number 31 – 4 = 27
other way is 40, thus missing number 40 -4 = 36

so there can be more such numbers