Cutting Territory

Consider a block of wood of dimensions $6\times8$ . Also, consider support rods of length $2$ , and negligible cross-section. Now, the wooden board can be cut , only if the cut is not obstructed by a support. Also, any successful cut must result in two pieces. If the smaller of the two pieces must always have an area less than $\frac{25}{4}$ , find the minimum number of supports required.

Details and Assumptions:

• A cut starts for one edge, and must end at another edge. No cut can be made solely in the interior of the board

• A cut must be linear, and cannot curve around supports

• Supports can be placed back-to-back, side-to-side, but not one superimposing the other

• The arrangement of the supports must allow cuts, and not completely eradicate the possibility of cuts