Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

I was asked the following puzzle for an interview.

There is a square sheet. A smaller square hole is made on it (at a random place). How can I divide the rest of the sheet into two halves (in terms of the total area)?

How to solve this?

share|cite|improve this question
up vote 11 down vote accepted

Draw a line joining the centers of the two squares and cut along that line.

share|cite|improve this answer
Works even if the two squares do not have parallel sides :-) – Henning Makholm Mar 5 '12 at 3:21
This also works for any figures for which there is a point such that all lines through the point divide the figure into two parts of equal area. The figures do not have to be the same shape, only that each has such a point and the line is drawn between the points. If the points coincide, any line through it will do. – marty cohen Mar 5 '12 at 5:46
And for n dimensions, take n objects each with a point such that any n-1 dimensional hyperplane divides it into two n-dimensional parts of equal n-dimensional volume. Then the n-1 dimensional hyperplane through these n centers divide each object and threfore the "holed" object into two parts of equal volume. – marty cohen Mar 5 '12 at 5:51

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.