11.1 Figure 1 has $a$ rectangles, find the value of $a$.

I1.2 Given that 7 divides 111111 . If $b$ is the remainder when $\underbrace{111111 \ldots 111111}_{a \text {-times }}$ is divided by 7 , find the value of $b$.

I1.3 If $c$ is the remainder of $\left\lfloor(b-2)^{4 b^{2}}+(b-1)^{2 b^{2}}+b^{b^{2}}\right\rfloor$ divided by 3 , find the value of $c$.
I1.4 If $|x+1|+|y-1|+|z|=c$, find the value of $d=x^{2}+y^{2}+z^{2}$.
$$
\begin{array}{l}
=111111 \times \underbrace{1000001 \cdots 1000001}_{161 ' s} \times 10000+7 \times 158+5 \\
=7 m+5 \text {, where } m \text { is an integer. } \\
b=5 \\
{\left[(5-2)^{100}+(4)^{50}+5^{25}\right]=3^{100}+4^{50}+5^{25}} \\
=3^{100}+(3+1)^{50}+(3 \times 2-1)^{25} \\
=3^{100}+3 m+1+3 n-1 \text { (by binomial theorem, } n, m \text { are integers) } \\
\end{array}
$$

The remainder $c=0$
$$
\begin{array}{l}
|x+1|+|y-1|+|z|=0 \\
x=-1, y=1 \text { and } z=0 \\
d=(-1)^{2}+1^{2}+0^{2}=2
\end{array}
$$