Basically bill wrote or chose a number. That number that he chose needed to have 2 things.
1. It needed to have been a number in between 27 and 45
2. It needed to have been an odd number in between 27 and 45.
There are only 2 possible choices that are odd, so eliminate the other 2 that are even. Next look at the 2 numbers that are odd.
The digits for each number must add up to 8.
35 - 3 + 5 = 8
43 - 4 + 3 = 7.
Which number adds up to 8. The digits in 35 or 43? It is 35.
Thus the final solution is 35. The number that Bill wrote.