MathDB

Let

k

and

N

be integers such that

k > 1

and

N > 2k + 1

. A number of

N

persons sit around the Round Table, equally spaced. Each person is either a knight (always telling the truth) or a liar (who always lies). Each person sees the nearest k persons clockwise, and the nearest

k

persons anticlockwise. Each person says: ''I see equally many knights to my left and to my right." Establish, in terms of

k

and

N

, whether the persons around the Table are necessarily all knights.
Sergey Berlov, Russia

C1

Problems(1)