The Association for the Construction, Development and Wellbeing of Nuclear Power Plants (or simply ACDWNPP for short) plans to build a new nuclear power plant in Checkerboard City. As you all surely know, the area of Checkerboard City is divided into 144 square blocks that are arranged in the form of a 12x12 checkerboard. For building the power plant, the ACDWNPP needs to purchase 12 of these blocks that form a 3x4 or 4x3 rectangular region.
The town council of Checkerboard City wants to protect Checkerboard City against this nuclear threat. The council decides to purchase a small number of blocks so that there remains no possibility for the ACDWNPP to get a 3x4 or 4x3 rectangular region (from the remaining blocks).
What is the smallest possible number of blocks that the town council needs to purchase?