How many squares are there in the figure shown below?

Correct — B. The drawing is made of twenty straight segments, ten horizontal and ten vertical, and the count only comes out if you work by size class instead of hunting at random.

Rule: count the one-cell squares, then the two-cell squares, then the outer boundary.

One cell wide: 9. Eight are the staircase cells that step down from the upper right to the lower left. The ninth is the small square cut where the detached top-left square crosses the outline's corner.

Two cells wide: 7. Two are stacked against the right-hand edge and two more sit inside the staircase.
The fifth is made of the two lowest staircase cells together with the flap hanging below the outline.
The last two are the detached top-left square itself and the large cell in the outline's top-left corner.

The whole outline: 1.

9 + 7 + 1 = 17, which is option (b).

Why the others are wrong

• (a)
  18 — 18 counts one square too many. The usual extra is the flap below the staircase, which is two cells wide but only one deep and so is a rectangle.
• (c)
  15 — 15 leaves out the outer boundary and the corner sliver — the two regions this card flags as debatable. The key counts both, which is what takes the total to 17.
• (d)
  16 — 16 is one short, and almost always because the outer outline was never counted: 9 + 7 stops at the two-cell squares.

A counting figure is a bookkeeping problem, not a test of eyesight. Fix an order — smallest size first, then each larger size — and no square gets counted twice or missed.

Two habits pay for themselves. A square needs equal sides, so a two-wide, one-deep region is a rectangle and does not count. And the outer boundary is itself a square, which is the one most often forgotten.

Overlapping outlines add a third habit: where two of them cross, the region they share can be a square in its own right.

Key facts

• The figure is built from exactly twenty straight segments: ten horizontal and ten vertical.
• On the key's count of 17, nine squares are one cell wide, seven are two cells wide, and one is the whole outer boundary.
• A region two cells wide and one cell deep is a rectangle, not a square, and must be left out of the count.

Common traps

• Counting the flap below the staircase as a square when it is two cells wide and only one cell deep.
• Leaving out the outer boundary, which lands you on 16.
• Treating the detached top-left square as decoration rather than as a square to be counted.

No directly related past PYQ was found.