Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given the dimensions of two rectangles, i need to know how many smaller rectangles can fit the bigger one. It should account for mixed orientations meaning that the smaller rectangle can both be landscape and portrait when fit inside the bigger rectangle.

Example image

Is there a math equation for this?


share|cite|improve this question
Going by how you've packed the rectangles in your image, it should say $2\times 5$ rectangles, not $3\times 5$. Also, you can fit eight of them in the $7\times 12$ rectangle by packing six along the length $12$ edge, and two more in the leftover space. – Rahul Jan 17 '12 at 10:26
thanks for the correction, will correct it soon. So how do i go about finding the optimal solution for this? – user1142924 Jan 17 '12 at 11:01
If I knew, I would have posted an answer. But someone else has... – Rahul Jan 17 '12 at 11:15

I don't think there's any "formula" for this and as far as I remember the problem is conjectured to be NP-hard, but not proven to be. For a heuristic that finds very good solutions (conjectured by the authors to be optimal), see this.

share|cite|improve this answer
what about finding how many could fit in x and how many could fit in y then we have how many could fit totally by multiplying the results – albanx May 12 '15 at 13:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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