MathDB

We assume a truck as a

1 \times (k + 1)

tile. Our parking is a

(2k + 1) \times (2k + 1)

table and there are

t

trucks parked in it. Some trucks are parked horizontally and some trucks are parked vertically in the parking. The vertical trucks can only move vertically (in their column) and the horizontal trucks can only move horizontally (in their row). Another truck is willing to enter the parking lot (it can only enter from somewhere on the boundary).
For

3k + 1 < t < 4k

, prove that we can move other trucks forward or backward in such a way that the new truck would be able to enter the lot.
Prove that the statement is not necessarily true for

t = 3k + 1

Problem Statement