At first glance, everything seems easy: a grid, some lines, and the answer seems obvious. Yet, this is often where we get trapped. Why? Because our brain loves to simplify images and omit hidden details. As a result, we stop too quickly, convinced we’ve seen it all. What if, in fact, the key was to slow down, observe differently, and let logic take over?

Why these grids trap us

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The problem is like a  puzzle game  : you get excited about it, then discover there are multiple levels. The 3×3 grid, for example, doesn’t just contain small, conspicuous squares. It also contains  discrete combinations  : medium-sized squares made up of 2×2 squares, and a large square encompassing the whole thing. If you don’t think about these groupings, you’re missing half the story. The good news is: there’s a simple way to count everything without missing anything.

Concentration test: can you find all the boxes?

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.