The Magic of 37

If x is a multiplication of 3 (3,6,9,12,15,....)

37 * x = y₁y₂y₃ = z

 y_{1 +} y_{2 +} y₃ = x
 y₁ = z div 100
 y₂ = (z mod 100) div 10
 y₃ = (z mod 10) div 1

Examples:
37*3 = 111
1+1+1 = 3

37*6 = 222
2+2+2 = 6

Interesting, isn't??

Not really so.   x is multiplication of 3, so x = 3*b (where b=1,2,3...)
37*x = 37 * (3*b) = 111*b = bbb

so bbb = y₁y₂y₃ = yyy

or y = b

When we do y₁ + y₂ + y₃, it is actually b + b + b.  For example, pick b=2 (so x=6), 111*b = 222, 2+2+2=6=x.