SAT1000 - P914

The 0-1 regular sequence $\{a_n\}$ is defined as follows:

• $\{a_n\}$ has $2m$ terms $(m \in \mathbb N^+)$ .

• Exactly $m$ terms are $0$ and $m$ terms are $1$ .

• $\forall k \geq 2m\ (k \in \mathbb N^+)$ , the number of $0$ 's is always greater or equal to the number of $1$ 's for subsequence $a_1,a_2,\cdots,a_k$ .

For $m=2020$ , the number of such 0-1 regular sequences is $M$ . Submit $\lfloor \log_2 M \rfloor$ .

Have a look at my problem set: SAT 1000 problems