How many right angles...

[glenngosack]

here's my solution (how I got the 58)

[Acorn]

here's my solution (how I got the 58)

Glenn, a good visual proof. Or 50, if the ones outside the shape are not included...
Acorn

[raden92]

54 from me
What is the right answer?

[Rik]

54 from me
What is the right answer?

I attached a zipped image in Post #9 that will help you to count the number of right angles.

[Acorn]

Rik, sorry to diss your answer but I'm now at over 120.
If a right angle is the meeting point between two perpendicular straight lines then there are nodes with a 90deg angle that can be formed by different straight lines; same node but different lines of construction.

By way of example, take the two red squares.
These have four distinct nodes, not touching any other coloured squares.
I can take any three of these nodes and demonstrate each defines a right angle.
I can do these four ways for these four nodes.

For all five overlapping squares, this leads to 32 extra right angles.
There are more subtle choices.

Good puzzle.

Acorn

[Igor01]

I think that 58 is OK



Igor

[Rik]

Rik, sorry to diss your answer but I'm now at over 120.
If a right angle is the meeting point between two perpendicular straight lines then there are nodes with a 90deg angle that can be formed by different straight lines; same node but different lines of construction.

By way of example, take the two red squares.
These have four distinct nodes, not touching any other coloured squares.
I can take any three of these nodes and demonstrate each defines a right angle.
I can do these four ways for these four nodes.

For all five overlapping squares, this leads to 32 extra right angles.
There are more subtle choices.

Good puzzle.

Acorn

Hi Acorn.

I've given an example of why it's 58, in Post #9.
Igor has also given an example of why it's 58, in Post #16.

So, I'd love to see a pictorial example of how you thing it's 120?
Assuming we all understand what a right angle is?!

[Acorn]

Hi Acorn.
I've given an example of why it's 58, in Post #9.
Igor has also given an example of why it's 58, in Post #16.
So, I'd love to see a pictorial example of how you thing it's 120?
Assuming we all understand what a right angle is?!

Rik, here goes...



Agree that there are 58 black dots so 58 right angles.

The second diagram applies my definition of a right angle in two aspects.

The first, if you were to make up the points A, B & C on a page, throw away your stencil then point B has a right angle between A and C: Angle ABC is valid in your drawing.
The second relies on the definition of a right angle uses two perpendicular straight lines.
Lines 1-2, 2-3 & 3-4 are all straight lines. Angle 123 is a right angle. Angle 124 is a right angle. Point 2 happens to have two co-incident right angles. Adding in all the relevant nodes for point 2, you end up with 9 co-incident right angles.

Acorn

[patmilz]

I also got 58

[Acorn]

I also got 58

Welcome to TalkGraphics,
acorn