Jump to content
BrainDen.com - Brain Teasers
• 0

# Packing squares, again

## Question

What is the area of the smallest square that holds five unit squares without overlap?

## Recommended Posts

• 0

I think the smallest square would be a 3 x 3.

If we start with the most compact area to contain 4 unit squares, it would be a 2 x 2 square. The addition of another unit square will force it to add at least one row or column - thus forcing you to a 2x3 configuration. To meet the criteria of the problem, we must expand that to a 3 x 3

There are multiple configurations [many are just reflections of others

# # #

# # -

- - -

or

# # #

# - -

# - -

or

# - #

- # -

# - #

or ...

##### Share on other sites

• 0

Place four unit squares into the corners of the resulting square and the 5th one into the middle after a 45 degree rotation.

The diagonal of the new square:
d=sqrt(2)+1+sqrt(2)

giving the surface 4.5+2*sqrt(2) (about 7.33).
Edited by harey

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Answer this question...

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
×
• ### Recently Browsing   0 members

• No registered users viewing this page.
×

• #### Activity

• Riddles
×
• Create New...