Final answer:
To construct a solid cube using the 1x2x6 rectangular blocks, Rene needs a minimum of 6 blocks.
Step-by-step explanation:
To construct a solid cube using the rectangular blocks, we need to use the principle that the number of blocks needed is equal to the volume of the cube divided by the volume of a single block.
Since each block has dimensions 1x2x6, its volume is 1x2x6 = 12 cubic units.
The volume of a cube with side length s is s^3. Since the blocks are 1 unit wide, we can stack 6 blocks to form the length and height of the cube, and 2 blocks to form the width. So, the volume of the cube is (6x1)x(6x1)x(2x1) = 72 cubic units.
Therefore, the smallest number of blocks Rene needs to construct a cube is 72/12 = 6 blocks.