Rabbit chase

[blamocur]

Found in an old book:

 

[blamocur]

I posted this problem because the answer in the book is wrong :

 

[Dr.Peterson]

Yes, I knew that the answer is simple in the case of 4 chasers, but didn't want to take to time to work out the n=3 case.

Mice problem - Wikipedia

en.wikipedia.org

It looks like they didn't pay attention to the difference.

 

[mario99]

Yes, I knew that the answer is simple in the case of 4 chasers, but didn't want to take to time to work out the n=3 case.

Mice problem - Wikipedia

en.wikipedia.org

It looks like they didn't pay attention to the difference.

Does Wikipedia has a typo?

It says that time [imath]\displaystyle = \frac{1}{1-\cos\frac{2\pi}{n}}[/imath] when actually this is the distance!

I posted this problem because the answer in the book is wrong :

View attachment 38664

Is the correct answer:

[imath]\displaystyle d_{3} = \frac{1}{1-\cos\frac{2\pi}{3}} = \frac{2}{3}[/imath]

?

Of course this distance is based on a unit side, so with a side of [imath]100[/imath] yards, the distance should be:

[imath]\displaystyle d = \frac{2}{3}100 = \frac{200}{3} \approx 66.67 \ \text{yards}[/imath]

 

[Dr.Peterson]

Does Wikipedia has a typo?

It says that time [imath]\displaystyle = \frac{1}{1-\cos\frac{2\pi}{n}}[/imath] when actually this is the distance!

Did you fail to read carefully what they said?

The most common version has the mice starting at the corners of a unit square, moving at unit speed.​

So time and distance are equivalent in their formulation. In one unit of time, they move one unit of distance.

 

[mario99]

Did you fail to read carefully what they said?

The most common version has the mice starting at the corners of a unit square, moving at unit speed.​

So time and distance are equivalent in their formulation. In one unit of time, they move one unit of distance.

You are right.

 

[blamocur]

Does Wikipedia has a typo?

It says that time [imath]\displaystyle = \frac{1}{1-\cos\frac{2\pi}{n}}[/imath] when actually this is the distance!


Is the correct answer:

[imath]\displaystyle d_{3} = \frac{1}{1-\cos\frac{2\pi}{3}} = \frac{2}{3}[/imath]

?

Of course this distance is based on a unit side, so with a side of [imath]100[/imath] yards, the distance should be:

[imath]\displaystyle d = \frac{2}{3}100 = \frac{200}{3} \approx 66.67 \ \text{yards}[/imath]

The book, published in 1971, predates Wikipedia by three decades I got 2/3 for the answer too.

 

[Dr.Peterson]

The book, published in 1971, predates Wikipedia by three decades I got 2/3 for the answer too.

And Wikipedia refers to books or articles from 1958 and 1877!

MathWorld gives a longer bibliography, going back to 1871.

 

[lookagain]

Does Wikipedia has a typo?

Does Wikipedia have a typo?

 

[mario99]

Does Wikipedia have a typo?

You are awesome professor lookagain. Thanks a lot for correcting my grammar. My cat has jumped on my keyboard and distracted me for 1 second while I was about to write "have", then my brain saw Wikipedia and wrote "has" automatically.

Cats should be caged!

 

[blamocur]

And Wikipedia refers to books or articles from 1958 and 1877!

MathWorld gives a longer bibliography, going back to 1871.

But the publishers in 1971 could not check Wikipedia, could they ?

 

[Dr.Peterson]

But the publishers in 1971 could not check Wikipedia, could they ?

They may well have seen the problem in some place like this (1959 -- I think I had this book as a kid, well before 1971):

​

​

​

That even covers that case of 3 pursuers, and gets it right.