The second question:

The third question:

The fourth question:

Solution: Assuming that the coloring scheme envisaged in the problem can be realized, the sum of the numbers representing points on each straight line should be odd, with five straight lines. Add five odd numbers representing the sum of the numbers on these five straight lines to get an odd sum. Every point in the picture is exactly on two straight lines at the same time. When calculating the above sum, the numbers representing each point are only added twice, so this sum should be an even number. This leads to contradictions, indicating that the hypothesis is not established and the dyeing scheme cannot be realized.

The fifth question:

This part of the extended material mainly examines the knowledge points of parity:

Parity is one of the basic properties of functions. If any x in the domain of function f(x) has f (-x) = f(x), then function f(x) is an even function. If any x in the definition domain of the function f(x) has f (-x) =-f(x), then the function f(x) is a odd function.

If f(-x)=-f(x) or f(-x)=f(x) cannot be true for any x in the function definition domain, then the function f(x) is neither a odd function nor an even function, and it is called an even-even function.

Parity is a global property of function, which is related to the whole domain. The domains of odd and even functions must be symmetrical about the origin. If the domain of a function is not symmetric about the origin, then the function must not be an odd (or even) function.