TOT 064 1984 Spring S-O5 S-A1 game with soldiers on a 20x20 table
Source:
August 19, 2019
game strategygameminimumcombinatoricssquare table
Problem Statement
(a) On each square of a squared sheet of paper of size there is a soldier. Vanya chooses a number and Petya moves the soldiers to new squares in such a way that each soldier is moved through a distance of at least (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 is this possible?
(Give the maximum possible , prove that it is possible to move the soldiers through distances not less than and prove that there is no greater for which this procedure may be carried out.)
(b) Answer the same question as (a), but with a sheet of size . (SS Krotov, Moscow)