# Smallest rectangle that fits the first 10 rectangles [closed]

What is the area of the smallest rectangle that can fit 10 rectangles with areas 1 to 10, inclusive? Rectangles must have integer sides and cannot overlap.

This answer seems a bit too trivial to be the intended one, but:

The minimum area must be 1+2+3+4+5+6+7+8+9+10=55

This can be done by taking rectangles of dimensions 1$$\times$$1, 2$$\times$$1,..., 10$$\times$$1 and arranging them in a straight line to get a rectangle with dimensions 55$$\times$$1

• Rot13(5k11 vf nyfb rkgerzryl fvzcyr (ebjf bs 10+1, 9+2, 8+3 rgp))
– Jafe
Jan 27 at 3:48
• Oh that's right, then it's just a poorly framed question Jan 27 at 3:52
• of course you are right. I completely stuffed up this question. It should have been a square... Jan 27 at 4:28

One example of smallest perimeter rectangle

Rectangle 8x7, with one empty 1x1 square, which is the nerest to an 8x8 square

• that's very nice! This is the question I should have asked. Jan 27 at 12:04