How many 2×2 subgrids (supercells) are there in a 4×4 grid?

Question

ScanSolve AI Tutor · Accepted Answer

To find the number of supercells, we first need to understand what a "supercell" refers to in this context. In grid-based problems, a "supercell" often refers to a subgrid of a specific size, commonly a $2 \times 2$ subgrid, unless otherwise defined. We will proceed with this common interpretation.

Determine the dimensions of the given grid.
The grid has 4 rows and 4 columns.
Define a "supercell".
Assuming a "supercell" is a $2 \times 2$ subgrid.
Calculate the number of possible $2 \times 2$ subgrids.
For a grid with $R$ rows and $C$ columns, the number of $k \times k$ subgrids is given by the formula $(R-k+1) \times (C-k+1)$ .
In this case, $R=4$ , $C=4$ , and $k=2$ .
Number of supercells = $(4-2+1) \times (4-2+1)$
Number of supercells = $(3) \times (3)$
Number of supercells = 9

The number of supercells (2x2 subgrids) in the given grid is 9.

How many 2x2 subgrids (supercells) are there in a 4x4 grid?

Answer

Step-by-step solution

Determine the dimensions of the given grid.

Define a "supercell".

Calculate the number of possible $2 \times 2$ subgrids.

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