perplexus.info :: Shapes : 100 squares

100 squares (Posted on 2006-04-30)

What is the fewest straight lines with which you can make exactly 100 squares?

For example with four vertical and five horizontal lines, evenly spaced, 20 squares are formed: twelve 1x1, six 2x2 and two 3x3.

 _____
|_|_|_|
|_|_|_|
|_|_|_|
|_|_|_|

Submitted by Jer

Rating: 4.0000 (3 votes)

Solution: (Hide)

15 lines is the minimum: 6 one way and 9 the other.
This makes a 5 by 8 array of small squares and the following totals:
1x1: 40
2x2: 28
3x3: 18
4x4: 10
5x5: 4
The grand total is 100 squares.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2023-09-07 07:36:11
Solution	Sparsh	2006-05-11 13:14:43
re: solution and discussion ==> A general formula	Ady TZIDON	2006-05-03 00:46:22
solution and discussion	Charlie	2006-04-30 20:10:08
re: 100	Leming	2006-04-30 17:35:53
100	Dej Mar	2006-04-30 17:25:24
Solution: spoiler	Leming	2006-04-30 17:16:37

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info