MathDB

4

Part of 1996 Cono Sur Olympiad

Problems(1)

Numbers in a sequence

Source: Cono sur Olympiad 1996 P4

10/7/2017
The sequence 0,1,1,1,1,1,....,10, 1, 1, 1, 1, 1,....,1 where have 11 number zero and 19951995 numbers one. If we choose two or more numbers in this sequence(but not the all 19961996 numbers) and substitute one number by arithmetic mean of the numbers selected, we obtain a new sequence with 19961996 numbers!!! Show that, we can repeat this operation until we have all 19961996 numbers are equal Note: It's not necessary to choose the same quantity of numbers in each operation!!!
algebracombinatorics