Solution to Puzzle #1

Solution Steps:

Let's call the original number 10x + y, where x is the tens digit and y is the ones digit.

1. From clue 2, we know:
   \( x + y = 9 \)

2. From clue 3, the reversed number is 10y + x.
   So, \( (10y + x) = (10x + y) + 27 \).
   Simplifying this:
   \( 10y + x = 10x + y + 27 \)
   \( 9y - 9x = 27 \)
   \( y - x = 3 \)

Now, solve the two equations: - \( x + y = 9 \) - \( y - x = 3 \)

Adding these equations: - \( 2y = 12 \) - \( y = 6 \)

Substitute \( y = 6 \) into \( x + y = 9 \): - \( x + 6 = 9 \) - \( x = 3 \)

So, the number is 36!