Count the number of squares in the given figure.

To count every square in a composite figure, classify the squares by how many of the smallest regions (components) each one is built from, from the smallest single-component squares up to the largest, and count every size-category exactly once so that no square is missed or counted twice.

The figure may be labelled as shown below.

1. The simplest, single-component squares: BCNM, CDON, PQJI and QRHI — 4 squares.

2. Squares made of 2 components each: MNTS, NOUT, STQP and TURQ — 4 squares.

3. Squares made of 5 components each: ACTL, CEFT, TFGI and LTIK — 4 squares.

4. Squares made of 6 components each: BDUS and SUHJ — 2 squares.

5. The single square made of 8 components: MORP — 1 square.

6. The single square made of 20 components: AEGK — 1 square.

Adding every size-category exactly once: 4 + 4 + 4 + 2 + 1 + 1 = 16. Re-grouping the same squares by orientation instead of by size — the axis-aligned squares (the four simplest squares, the two 6-component squares, the 8-component square and the full 20-component outer square) total 8, and the 45-degree tilted squares (the four 2-component squares and the four 5-component squares) total 8 — giving the same 16 overall, confirming that no square has been missed or double-counted. Hence the figure contains 16 squares in total.