MathDB

Consider all possible functions defined for

x = 1, 2, ..., M

and taking values

​​y = 1, 2, ..., n

. We denote the set of such functions by

T.

T_0

we denote the subset of

T

consisting of functions whose value changes exactly by

1

(in one direction or another) when the argument changes by

1

. Prove that if

M\ge 2n-4

, then among the functions from of the set

T

, there is a function that coincides at least at one point with any function from

T_0

. Specify at least one such function. Prove that if

M <2n-4

, then there is no such function.

Problem Statement