15. How many three-digit numbers are there in which any two adjacent digits differ by 3 ?
A 12
B 14
C 16
D 18
E 20
15. E The first digit can be anything from 1 to 9 . Where possible, we can reduce this by three or increase it by three to get the next digit, giving the following possibilities for the first two digits: $14,25,30,36,41,47,52,58,63,69,74,85,96$. Repeating for the third digit, we obtain the possibilities in numerical order: 141, 147, 252, $258,303,363,369,414,474,525,585,630,636,696,741,747,852,858,963$, 969 , which is 20 options.