(a) On each square of a squared sheet of paper of size 20×20 there is a soldier. Vanya chooses a number d and Petya moves the soldiers to new squares in such a way that each soldier is moved through a distance of at least d (the distance being measured between the centres of the initial and the new squares) and each square is occupied by exactly one soldier. For which d is this possible?
(Give the maximum possible d, prove that it is possible to move the soldiers through distances not less than d and prove that there is no greater d for which this procedure may be carried out.)
(b) Answer the same question as (a), but with a sheet of size 21×21. (SS Krotov, Moscow) game strategygameminimumcombinatoricssquare table