# Catbird Seat problem

From Futility Closet:

A ladder is leaning against a tree. On the center rung is a pussycat. She must be a very determined pussycat, because she remains on that rung as we draw the foot of the ladder away from the tree until the ladder is lying flat on the ground. What path does the pussycat describe as she undergoes this indignity?

I like this illustration and description of the problem even more than the solution.

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1. nixiebunny says:

The cute censorship overlay doesn’t go away when I click on it. I guess we’re all doomed now.

I had to hold my hand up to a vertical surface to impersonate a ladder,  and hold a finger at the middle of my hand to impersonate the cat, to see the path. It is quite non-intuitive, but math questions rarely are intuitive. My math brain told me that sines and cosines were involved, so I was expecting something curvy.

2. I don’t know, it looks like an inverted catenary to me.

1. huh huh…. CATernary.    I came to give that answer and found yours – then I checked – WERE BOTH WRONG!

3. RufusTheGreat says:

Trick question, cats can’t talk.  Therefore they don’t describe anything.

1. rabidpotatochip says:

Cats can talk, it’s just that us humans can’t understand a word they’re saying.  Just ask any one of them!

1. irksome says:

*feed me*

1. rabidpotatochip says:

See? Complete gibberish.  ;)

4. Susan Carley Oliver says:

OK, I want a whole book of *this* kind of story problems!

1. alephxero says:

I don’t think the cat would put up with this crap for a whole book of story problems.

5. I know the answer, only because I just worked on a mechanism like this, which turns vertical motion into horizontal motion and vice-versa. Hint: unlike almost everything on a cat’s body, the answer cannot be described as triangular.

6. Trick question, no cat would  stay willing put on a moving ladder.

1. Lobster says:

What if it’s a Norwegian Bluehair?

7. Some cats are surprisingly tolerant/lazy/stubborn, and will put up with a surprising amount of displacement before trying to scratch your face off.  I used to own a cat which would curl up precisely where she wasn’t supposed to (on a recently-used stove-top, on top of the TV, in the airing cupboard), paws tucked underneath, and it got to the point where I would just sigh, scoop her up on both hands, and transfer her to a more appropriate spot.  Sometimes, she would barely bother to wake up.  She would have been a good model for a live demonstration of the cat-burdened-tree-leaning ladder experiment.

1. Marktech says:

Some cats are surprisingly tolerant/lazy/stubborn, and will put up with a surprising amount of displacement before trying to scratch your face off.

[There now follows a Physics Joke.]

Would such a cat have a particularly high mew?

[That was a Physics Joke.  Thank you, I’m here all week.  Try the veal.]

8. Quothz says:

Trick question: When you pull on the ladder, the foot catches in the soft ground, levering the ladder over you and down atop you. The cat steps on your face as she saunters away.

9. KWillets says:

Not too hard.  I think the non-center case is used for drawing an eccentric version of the figure.

1. KWillets says:

In fact here’s an article on that method:  http://www.finehomebuilding.com/articles/article.aspx?id=62918&nterms=61998,65726

10. peregrinus says:

The path the cat describes is the route to Hell she will force the mover of the ladder down, and precisely how she will prod them along it, if only humans could be the size of mice, ffs, and don’t touch my fur you f*ck.

11. Smoakes says:

Didn’t believe the answer until I held a pen (the cat) between two knuckles (my fingers were the ladder) and moved it along a piece of paper… the answer sure is correct and I STILL can’t make sense of it in my head.

12. dman says:

Rather than the maths-y solution on the site, I solved it originally by picturing a *string* tied to the bottom of the tree, and the cat.
When the ladder is fully vertical, the string is taut. Also when it finishes flat on the ground. Also … at any point in the path.

This is proven because at any time, the angle and distance from string->cat is identical to the angle from the foot of the ladder to cat. The distance from the foot of the ladder doesn’t change, so the taut string doesn’t change either. The string describes an arc (radius half-a-ladder)

13. Barry Stock says:

It’s either a Papaya (Carica papaya) or a Breadfruit tree (Artocarpus altilis). The problem with the cat could be solved by wrapping it in papaya leaves, which contain papain, a natural meat tenderizer.

14. dr says:

Change frames.  If you fix the foot of the ladder, and imagine the tree moving, the cat obviously traverses a circular arc.  Now, translate your point of view back to the tree, a translated circle is still a circle.

1. rabidpotatochip says:

Great explanation.  Thanks.

What finally did it for me was an old art project we did way back in the day with string on paper.  The first piece of string has the maximum possible Y and an X of 1, the second has maximum Y – 1, and X of 2, etc. until you hit the bottom.  Despite every piece of string being straight you eventually end up with a curve.