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 composite 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. Squares made of 2 components each: BJMI, CKMJ, DLMK and AIML — 4 squares.

2. Squares made of 3 components each: EBMA, BFCM, MCGD and AMDH — 4 squares.

3. Squares made of 4 components each: VWBA, XYCB, ZA1DC and B1C1AD — 4 squares.

4. Squares made of 7 components each: NOJL, PQKI, RSLJ and TUIK — 4 squares.

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

6. The single square made of 12 components: EFGH — 1 square.

Adding every size-category exactly once: 4 + 4 + 4 + 4 + 1 + 1 = 18. Re-grouping the same squares by increasing side length — the smallest tilted squares first, then each larger tilted set, then the two large upright squares — gives the identical six groups and the same total, confirming that no square has been missed or double-counted. Hence the figure contains 18 squares in total.