MathDB

Celeste has an unlimited amount of each type of

n

types of candy, numerated type 1, type 2, ... type n. Initially she takes

m>0

candy pieces and places them in a row on a table. Then, she chooses one of the following operations (if available) and executes it:

1.

She eats a candy of type

k

, and in its position in the row she places one candy type

k-1

followed by one candy type

k+1

(we consider type

n+1

to be type 1, and type 0 to be type

n

2.

She chooses two consecutive candies which are the same type, and eats them.
Find all positive integers

n

for which Celeste can leave the table empty for any value of

m

and any configuration of candies on the table.

<span class='latex-italic'>Proposed by Federico Bach and Santiago Rodriguez, Colombia</span>

Problem Statement