2. Jenny is going to attend a seven-day sports training camp, where each day she must and can only participate in one of the training sessions for ice hockey, tennis, or field hockey, and in any consecutive four days, she must participate in all three types of training. Find the number of different training schedules Jenny can have over the seven days, and prove your conclusion.
2. The problem is equivalent to arranging the elements of the set $\{X, Y, Z\}$ in seven positions, such that any permutation of length 4 contains the elements $X$, $Y$, and $Z$.
For $n \geqslant 4$, we define:
(1) Let $f_{n}$ be the number of different permutations of length $n$ that end with $A B C$, where $A B C$ represents a permutation of $X$, $Y$, and $Z$.
(2) Let $g_{n}$ be the number of different permutations of length $n$ that end with $A B C$, where $B$ and $C$ are different and $A$ is the same as $B$ or $A$ is the same as $C$.
(3) Let $h_{n}$ be the number of different permutations of length $n$ that end with $A B C C$, where $A B C$ represents a permutation of $X$, $Y$, and $Z$.
Then $f_{4}=6 \times 3=18$,
$g_{4}=6 \times 2=12$,
$h_{4}=6$.
Notice that, for $n \geqslant 4$,
$$
\begin{array}{l}
f_{n+1}=f_{n}+g_{n}, \\
g_{n+1}=f_{n}+h_{n}, \\
h_{n+1}=f_{n} .
\end{array}
$$

From the above recurrence relations, we get Table 1.
Table 1
\begin{tabular}{|c|c|c|c|}
\hline$n$ & $f_{n}$ & $g_{n}$ & $h_{n}$ \\
\hline 4 & 18 & 12 & 6 \\
\hline 5 & 30 & 24 & 18 \\
\hline 6 & 54 & 48 & 30 \\
\hline 7 & 102 & 84 & 54 \\
\hline
\end{tabular}

Therefore, the number of different training schedules Jenny can have over seven days is
$$
f_{7}+g_{7}+h_{7}=102+84+54=240 \text {. }
$$