How many squares are there in the figure shown below?

Correct — C. Sort the squares by side length and count each length to exhaustion.

One cell wide: 5 — the four cells of the 2 by 2 block on the right, plus the cell to the left of that block's lower row.

Two cells wide: 5 — the block itself, two stacked at the right edge, one at the bottom left, and one closing off the big square's top-left corner.

At the top left: 2 — the small square that juts out, and the patch where it crosses the big square.

The big square itself: 1

5 + 5 + 2 + 1 = 13 — option (c).

Why the others are wrong

• (a)
  14 — 14 counts one shape too many. The 2 by 2 arrangement also contains 1 by 2 and 2 by 1 strips, and a strip has four corners but unequal sides.
• (b)
  12 — 12 is what you get by counting the two overlapping squares at the top left and walking past the small square where they cross. That patch is a square in its own right.
• (d)
  11 — 11 misses more than one size. The five one-cell squares and the five two-cell squares already reach ten, before the top-left pair and the big square itself are added.

Counting figures is a bookkeeping problem, not a spotting problem. Sort by size, count each size completely, then add.

Two errors dominate. Composite squares get missed — a 2 by 2 arrangement of cells is a square in its own right, as well as the four cells inside it. And rectangles get counted: a 1 by 2 strip is not a square.

A third error is specific to this drawing. Two squares overlap, and the region they share is closed on all four sides and is a square too, even though no single stroke draws its outline.

Key facts

• The drawing holds five squares one cell wide and five of double that side.
• The small square at the top left overlaps the big one, and the patch they share is closed on all four sides and counts as a square of its own.
• The outer boundary of the whole drawing is the thirteenth square.
• A 1 by 2 rectangle inside the grid has unequal sides and must not be counted.

Common traps

• Missing the square formed where two drawn squares overlap
• Counting the cells of a 2 by 2 arrangement but not the arrangement itself
• Including 1 by 2 rectangles, which is how the drawing yields 14 instead of 13

No directly related past PYQ was found.