How many rectangle(s) with two “#” is/are there in the figure below?

enter image description here

I tried to count it and my answer is 36.

My teacher shared the answer and ask us to find the reason why.

He said it is just

$2 * 3 * 2 * 3 $

I found out that my answer is correct. But, what do these factors mean?


Give numbers on the horizontal (up to down) and vertical (left to right) lines(not squares!).

Then the left/right side of the rectangle must be column $1,2,3$/column $4,5,6$. So, there are $9$ possibilities.

The upper/lower side of the rectangle must be row $1,2$/row $4,5$. So, there are $4$ possibilities.

Then, the whole possibilities are $3$6.

The two 2 means there are $2$ cases each to determine the upper/lower sides, and two 3 means there are $3$ cases each, to determine the left/right sides.

  • $\begingroup$ Thank you for the answer but I did some updates. $\endgroup$
    – PRD
    Oct 22 at 16:55
  • $\begingroup$ @PRD I edited my answer. See the last part! $\endgroup$ Oct 22 at 16:59
  • $\begingroup$ @Nightflight Thank you very much! $\endgroup$
    – PRD
    Oct 22 at 17:00
  • $\begingroup$ @PRD I'll say the upper/lower cases(left/right cases are exactly same way). There are 4 possibilities, $(U,L)=(1,4), (1,5), (2,4), (2,5)$. $\endgroup$ Oct 22 at 17:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.