perplexus.info :: Just Math : Squares and Rectangles II

Squares and Rectangles II (Posted on 2015-01-16)

(A) How many squares are there in the diagram given below?
(B) How many rectangles are there in the diagram given below?

+-----+-----+-----+-----+
|     |     |     |     |
|     |     |     |     |
+-----+-----+-----+-----+ 
|     |     |     |     |
|     |     |     |     |
+-----+-----+-----+-----+ 
|     |     |     |     |
|     |     |     |     |
+-----+-----+-----+-----+  
|     |     |     |     |
|     |     |     |     |
+-----+-----+-----+-----+  
      |     |     |     |
      |     |     |     |
      +-----+-----+-----+ 
            |     |     |
            |     |     |
            +-----+-----+ 
                  |     |
                  |     |
                  +-----+

*** If the length and width appear equal, then it is a square. If not, then it is a rectangle.

** The number of rectangles should exclude the ones that are counted as squares

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

detail on the rectangle counts

Comment 2 of 2 |

(In reply to A quick count. by Jer)

The rectangle counts are the same as Jer provided. I've added the two numbers, horizontal and vertical, that are multiplied to produce the product in the given square:

+-----+-----+-----+-----+
|  4  |  3  |  2  |  1  |
|  4  |  5  |  6  |  7  |
| 16  | 15  | 12  |  7  |     50
+-----+-----+-----+-----+ 
|  4  |  3  |  2  |  1  |
|  3  |  4  |  5  |  6  |
| 12  | 12  | 10  |  6  |     40
+-----+-----+-----+-----+ 
|  4  |  3  |  2  |  1  |
|  2  |  3  |  4  |  5  |
|  8  |  9  |  8  |  5  |     30
+-----+-----+-----+-----+  
|  4  |  3  |  2  |  1  |
|  1  |  2  |  3  |  4  |
|  4  |  6  |  6  |  4  |     20
+-----+-----+-----+-----+  
      |  3  |  2  |  1  |
      |  1  |  2  |  3  |
      |  3  |  4  |  3  |     10
      +-----+-----+-----+ 
            |  2  |  1  |
            |  1  |  2  |
            |  2  |  2  |      4
            +-----+-----+ 
                  |  1  |
                  |  1  |
                  |  1  |      1
                  +-----+
                             155

Posted by Charlie on 2015-01-16 10:10:39

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