The answer is 126 rectangles.
If you counted 18, you counted only the small rectangles you can see at first glance — 6 rows × 3 columns = 18 little boxes. But every rectangle made by combining boxes counts too: the doubles, the tall ones, the wide ones, and the one giant rectangle that is the whole grid itself. Here is the proof, and it works every time:
- Pick the left and right edges: The grid has 4 vertical lines. Any rectangle needs 2 of them. Choose 2 of 4 vertical lines = 6 ways.
- Pick the top and bottom edges: The grid has 7 horizontal lines. Any rectangle needs 2 of them. Choose 2 of 7 horizontal lines = 21 ways.
- Multiply them: Every pair of vertical lines can combine with every pair of horizontal lines to make exactly one rectangle. 6 × 21 = 126.
That is the whole grid — there are no diagonals, no gaps and no extra shapes hiding a bonus rectangle in the frame. If you landed on 18, you stopped at the smallest size. If you landed anywhere under 100, you found some of the combined rectangles but not every pairing of lines. The full, provable count is 6 ways × 21 ways = 126.
Did you trust the multiplication, or did you try to count them one by one? Be honest in the comments — and watch our page for tomorrow’s counting game.
