Question 10
Suppose that a number of $5\times7$ rectangles are placed on a large grid of unit squares so that each rectangle covers exactly $35$ of the unit squares. The rectangles can be placed either horizontally or vertically and they may overlap. Find the largest integer $N$ for which it is not possible to cover exactly $N$ unit squares in this way. [5 marks]
Investigation. Suppose instead we have rectangles of a single size $3\times n$, for some positive integer $n\ge6$. Placing them on the grid as above, what is the largest integer $N$ for which it is not possible to cover exactly $N$ unit squares? [4 bonus marks]
The original Investigation is assessed separately from the 35 base marks and the five-point main rubric.
Investigation. Suppose instead we have rectangles of a single size $3\times n$, for some positive integer $n\ge6$. Placing them on the grid as above, what is the largest integer $N$ for which it is not possible to cover exactly $N$ unit squares? [4 bonus marks]
The original Investigation is assessed separately from the 35 base marks and the five-point main rubric.