MathDB

Let

k

be a fixed positive integer,

k \le 10

. Given a list of ten numbers, the allowed operation is: choose

k

numbers from the list, and add

1

to each of them. Thus, a new list of ten numbers is obtained. If you initially have the list

1,2,3,4,5,6,7,8,9,10

, determine the values of

k

for which it is possible, through a sequence of allowed operations, to obtain a list that has the ten equal numbers. In each case indicate the sequence.

Problem Statement