MathDB

Divide a circle into

2n

equal sections. We call a circle filled if it is filled with the numbers

0,1,2,\dots,n-1

. We call a filled circle good if it has the following properties:

i

. Each number

0 \leq a \leq n-1

is used exactly twice

ii

. For any

a

we have that there are exactly

a

sections between the two sections that have the number

a

in them.
Here is an example of a good filling for

n=5

(View attachment) Prove that there doesn’t exist a good filling for

n=1399

P6