Let's observe the pattern used to code 'HILTON' as 'I T H L N O':
- The first letter 'H' is moved to the second position.
- The second letter 'I' is moved to the first position.
- The third letter 'L' stays in the same position.
- The fourth letter 'T' is moved to the third position.
- The fifth letter 'O' is moved to the fifth position.
- The sixth letter 'N' stays in the sixth position.
Now applying the same pattern to 'BILLION':
- The first letter 'B' is moved to the second position.
- The second letter 'I' is moved to the first position.
- The third letter 'L' stays in the same position.
- The fourth letter 'L' is moved to the third position.
- The fifth letter 'I' is moved to the fifth position.
- The sixth letter 'O' stays in the sixth position.
- The seventh letter 'N' stays in the seventh position.
Thus, 'BILLION' is coded as 'IBLLION'.
Therefore, the correct answer is \( \boxed{3} \).