cancel
Showing results for
Did you mean:
cancel
Showing results for
Did you mean:

Community Tip - Learn all about the Community Ranking System, a fun gamification element of the PTC Community. X

20-Turquoise

## Find the number of rectangles 2.

I find very good puzzle from YouTube and show it. Then I made new puzzle to find the number of rectangles of stair-like figures shown here. How to calculate the total number of rectangles included in this figure? I have no formula to calculate this answer, now.

First one, m=3 has 11 rectangles.

Second one, m=5 may have 54 rectangles.

1 ACCEPTED SOLUTION

Accepted Solutions
24-Ruby V
(To:ttokoro)

@ttokoro wrote:

I find very good puzzle from YouTube and show it. Then I made new puzzle to find the number of rectangles of stair-like figures shown here. How to calculate the total number of rectangles included in this figure? I have no formula to calculate this answer, now.

First one, m=3 has 11 rectangles.

Second one, m=5 may have 54 rectangles.

Here you are ( m = 2*n+1)

My function "countRect" works via brute force and could deal with any cloud of points in a grid.

But once you know the first few numbers you can search for the sequence and of course you find it in OEIS: https://oeis.org/A213840

The "n" used in OEIS is "my n" plus one.

3 REPLIES 3
24-Ruby V
(To:ttokoro)

@ttokoro wrote:

I find very good puzzle from YouTube and show it. Then I made new puzzle to find the number of rectangles of stair-like figures shown here. How to calculate the total number of rectangles included in this figure? I have no formula to calculate this answer, now.

First one, m=3 has 11 rectangles.

Second one, m=5 may have 54 rectangles.

Here you are ( m = 2*n+1)

My function "countRect" works via brute force and could deal with any cloud of points in a grid.

But once you know the first few numbers you can search for the sequence and of course you find it in OEIS: https://oeis.org/A213840

The "n" used in OEIS is "my n" plus one.

20-Turquoise
(To:Werner_E)

24-Ruby V
(To:ttokoro)

Here are some animations 😉

Some random points:

Announcements
Top Tags