Math Is Fun Forum

Kurre

Member

Registered: 2006-07-18

Posts: 280

2 Juggling problems

A while ago I created and posted a lot of juggling riddles and math problems on a juggling forum. These two were the only ones that no one solved (at least not until the whole section got locked ):

Some basic info on juggling: http://en.wikipedia.org/wiki/Juggling
just a few videos so you know how it looks like:
http://www.youtube.com/watch?v=ZNU96CJMdy4
http://www.youtube.com/watch?v=2o9nnHK1YG8
http://www.youtube.com/watch?v=pU7uobOMVyU&feature=related
(in basic patterns, odd numbers cross(cascade), even dont(fountain) i.e dont switch hands)

1: A juggler juggles 7 rings that are black on one side and white on the other side. When he begins, all rings has the white side turned to the audience. The juggler starts counting on the first catch and turns a ring if he counts a prime number. Show that after the second catch it will never occur again that all rings has their white side turned to the audience at the same time.

2: N objects are juggled in the basic patterns (fountain/cascade). Let S(x) be the sum of all heights of the objects at any moment x. Is S(x) constant? otherwise, when does maximum occur?

(we approximate the switch of objects in the hands, so when one object is thrown and one caught they just switch places instantly with no lost time and no empty hands. Also the hands dont move while throwing, so when the hands hold a ball, we think of the height as constant)

enjoy!

Last edited by Kurre (2008-01-24 00:58:15)