24. Arrange the numbers $1,2,3,4,5$ in a circle. If there exists an integer $n(1 \leqslant n \leqslant 15)$, such that the sum of any consecutive numbers in the arrangement is not equal to $n$, then the arrangement is called a "bad arrangement". For circular arrangements obtained by rotation or reflection, they are considered the same arrangement. Then there are ( ) different bad arrangements.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
24. B.

The number of circular permutations of the numbers $1, 2, 3, 4, 5$ arranged on a circle is $4!=24$. Next, verify which of these are bad permutations.

If $n \in \{1,2,3,4,5\}$, then in any circular permutation, there is a number that equals $n$;

If $n=15$, then the sum of all numbers in any circular permutation equals $n$;

If $n \in \{10,11,12,13,14\}$, then in any circular permutation, removing the number $15-n$ results in a sum of the remaining numbers equal to $n$;

If $n=6$, then a permutation is not bad if it contains the sequence of three consecutive numbers $1,2,3$, or if it contains the pairs $2, 4$ or $1, 5$. Since circular permutations that are rotations or reflections of each other are considered the same, there is only one bad permutation (as shown in Figure 10);

If $n=9$, when a part of the consecutive numbers in a circular permutation sums to 6, the remaining part sums to 9, so the bad permutation is also as shown in Figure 10;

Similarly, if $n=7$ or 8, there is also only one bad permutation (as shown in Figure 11).
In summary, there are two "bad permutations".