MathDB

Several positive integers

a_0 , a_1 , a_2 , ... , a_n

are written on a board. On a second board, we write the amount

b_0

of numbers written on the first board, the amount

b_1

of numbers on the first board exceeding

1

, the amount

b_2

of numbers greater than

2

, and so on as long as the

b

s are still positive. Then we stop, so that we do not write any zeros. On a third board we write the numbers

c_0 , c_1 , c_2 , ...

. using the same rules as before, but applied to the numbers

b_0 , b_1 , b_2 , ...

of the second board. Prove that the same numbers are written on the first and the third boards.
(H. Lebesgue - A Kanel)

Problem Statement