MathDB

3

Part of 1989 National High School Mathematics League

Problems(2)

Figure of Function

Source: 1989 National High School Mathematics League, Exam One, Problem 3

2/25/2020
For any function f(x)f(x), in the same rectangular coordinates, figures of function y=f(x−1)y=f(x-1) and y=f(−x+1)y=f(-x+1) (A)\text{(A)} are symmetrical about xx-axis (B)\text{(B)} are symmetrical about line x=1x=1 (C)\text{(C)} are symmetrical about line x=−1x=-1 (D)\text{(D)} are symmetrical about yy-axis
functionanalytic geometry
Square Table

Source: 1989 National High School Mathematics League, Exam Two, Problem 3

2/25/2020
Given n×nn\times n square table, fill in each square with −1-1 or 11. For nn squares that any two of them are neither in the same line nor in the same column, we call the product of the numbers in the squares basic term. Prove that she sum of all basic terms is always a multiple of 44.