The step-by-step method for counting squares
Start with the most obvious: single-cell squares. In a 3×3 grid, there are 9 of them (one per cell). Next, locate the medium-sized 2×2 squares. How many can you fit? Imagine dragging a 2×2 square inside the grid: it can start at the top left, in the top middle, left center, etc. In total, there are 4. Finally, add the giant square that covers the entire grid: 1. So, we get 9 + 4 + 1 = 14. And there you have it! No need for a magnifying glass, just a little observation routine.
The mnemonic trick that changes everything
Remember this mini-ritual: “small, medium, large .” First the small (all the 1×1 squares), then the medium (all the 2×2), and finally the large (the 3×3). This sequence avoids duplicates and omissions. For a 4×4 grid, we decline: small (16), medium (9), large medium (4, because 3×3), then the giant (1, the 4×4). Add: 16 + 9 + 4 + 1 = 30. We’re already making progress!
A little extra for those curious about logic
Want a general rule ( I promise, it’s as simple as whipping egg whites )? In an n×n grid, the total number of squares is the sum of 1² + 2² + … + n². In other words, you add up the squares of all possible sizes. For n = 3: 1² (9 times 1) + 2² (4) + 3² (1) = 14. This formula becomes second nature and gives a real sense of mastery, like making a smooth pancake batter the first time.
A fun variation to challenge yourself
Do you like the 3×3 version? Try decorative diagonals (thin oblique lines): they don’t create new squares, but they do confuse perception. Another idea: print a grid and color each square you find a different color (blue for the small ones, purple for the medium ones, black for the large one). Visualizing the families of squares helps to establish logic and makes the exercise really fun , to do alone or with the children.
A little boost for daily attention
These mini-tests are the equivalent of a morning stretch for the mind: a few minutes are enough to awaken selective attention, strengthen concentration and stimulate visual acuity. Slip one into your coffee routine, between two emails or on the subway; like a Sudoku or a crossword puzzle, the satisfaction of finally “seeing” the 14 squares is pleasant … and makes you want to do it again.
