Twelve Glowing Dots
Read the puzzle
Twelve dots sit on a 4 by 4 grid with the four corner dots missing, forming a plus shape. Row 1 has dots in columns 2 and 3; rows 2 and 3 have dots in all four columns; row 4 has dots in columns 2 and 3. How many squares can you make by joining 4 dots?
How many squares can you make by joining 4 dots?
Don't forget squares standing on a corner.
11
5 upright squares and 6 tilted ones.
How to solve it
Sort the squares by shape and count each group, so none is counted twice or missed.
Upright squares first. There are five 1-by-1 squares: the centre one, plus one in each arm of the plus. No bigger upright square fits, because a 2-by-2 or 3-by-3 square would need a missing corner dot.
Next, squares standing on a corner whose sides go one step across and one step up or down. Each one surrounds one of the four middle dots, so there are 4 of them.
Then the larger tilted squares whose sides go two steps across and one step up or down. Their corners use the outer dots of the plus, and there are 2 of them, one leaning each way.
Total: 5 + 4 + 2 = 11 squares.
The usual wrong answer is 5, from counting only upright squares, or 9, from missing the two big tilted ones. Quick check: all four corners of a square must be dots, so trace each candidate side by side before counting it.
Learn the method: How Many Squares Puzzle: Count Squares, Rectangles and Triangles
