In an office with 4 people, the 1 manager always lies and the 3 engineers always tell the truth. **Who is the manager?**

**Alice:** "Bob is an engineer."

**Bob:** "Alice is an engineer."

**Carol:** "David is the manager."

**David:** "Carol is the manager."

**Alice:** "David is the manager."

**David:** "Alice is the manager."

**True or False?**

\[\large 1\div\Big(2\div (3 \div (4\div ( \cdots \div (2015\div (2016\div 2017) ) \cdots \Big) > 1\]

\(1\) is an \(\color{red}\text{odd}\) number.

\(1 + 2 \) is an \(\color{red}\text{odd}\) number.

\(1 + 2 + 3\) is an \(\color{blue}\text{even}\) number.

\(1 + 2 + 3+ 4\) is an \(\color{blue}\text{even}\) number.

\(1 + 2 + 3+ 4+5\) is an \(\color{red}\text{odd}\) number.

\(\cdots \cdots\)

**True or False?**

\(1 + 2 + 3 + \cdots + 999 \) is an \(\color{red}\text{odd}\) number.

A rectangle is divided into nine sub-rectangles, as shown in the figure. Inside some rectangles are their respective **perimeters**.

**What is the perimeter of the large, outer rectangle?**

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