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

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