How many rectangles are in a 2X3 grid?

Question

ITS NOT 6 BELIEVE ME

Answer 1

i found 18..

Answer 2

18
assuming the grid contains 6 shapes with 1x1 sides each.

One of the keys for solving this is remembering that squares are also rectangles (i.e. shapes with 90 degrees angle), but rectangles called "special case", because their all sides are of equal length.

Here you have it:

first - the big one (2x3) = 1 rect.

then - looking from top, there's one rectangle (2x2), and another one (2x2) looking from the bottom = 2 rectangles

then, 2 halves (by longer side), one 1x3 shape to the left, and the other one to the right (2x 1x3) = 2 rects

then, each of the halves contains 2 shapes, dim: 2x1 = 2 rect. for the left, and 2 rect. for the right = 4 rect.s
(first time look from the top to bottom, then look from bottom to top - you'll see one 1x2 rectangle in each turn, so this makes 2 rectangles => this goes for e.g. left half, and repeat that for the right half, and you'll see another 2 rectangles, which makes the total of four rectangles)

then, by rows - there are 3 rows, aka = 3 rectangles (2x1 each)

and finally (someone would start from here, probably), 6 smallest rectangles, aka 6 shapes 1x1 = 6

to sum up: 1 + 2 + 2 + 4 + 3 + 6 = 18

Have I missed a rectangle or two? Checked everything more than twice, but curious to find out more ;D

Answer 3

It happens that I was working on a similar problem yesterday.

One can show that, in general, the number of rectangles in an m x n grid is (m * (m + 1) * n * (n + 1))/4.

In this case, then, we have (2 * (3) * 3 * (4))/4 = 18 rectangles.

Answer 4

Two rectangles

Answer 5

ooo
ooo

6+3+4+2+2+1=18

EDIT: I think you forgot squares or 3x1 Mn

Answer 6

6+1+3+4+2 = 16

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Found two more - I also vote for 18