MathDB

a) What is the least number of points that can be chosen on a circle of length

1956

, so that for each of these points there is exactly one chosen point at distance

1

, and exactly one chosen point at distance

2

(distances are measured along the circle)?
b) On a circle of length

15

there are selected

n

points such that for each of them there is exactly one selected point at distance

1

from it, and exactly one is selected point at distance

2

from it. (All distances are measured along the circle.) Prove that

n

is divisible by

10

Problem Statement