Problem of the Block
Block 3
Chameleons
(from the literature) On the island of Camelot, there are 45 chameleons. At one time 13 of them
were grey, 15 brown, and 17 crimson. However, whenever two chameleons of different color meet,
the both change color to the third color. Thus, for example, if a grey and a brown chameleon were
to be the first to meet, the count would change to 12 grey, 14 brown, and 19 crimson.
1. Is it possible to arrange a succession of meetings that would result in all chameleons displaying
the same color?
2. On the nearby island of Camelittle, there are four colors of chameleons, namely grey, brown,
crimson, and white. In Camelittle, when two chameleons of different colors meet, they change
colors to the remaining two colors in a way that they still are differ. For example, if a grey
and brown chameleon meet, one of the chameleons would turn crimson and one would turn
white.
(a) Is there an initial collection of chameleons such that the collection has at least one
chameleon of each color such that there is no succession of meetings that would result in
a collection of chameleons consisting of just two colors?
(b) Is there an initial collection of chameleons such that the collection has at least one
chameleon of each color such that there is a succession of meetings that would result in
a collection of chameleons consisting of just two colors?
3. In addition to the above two problems, pose a problem of your own related to color changing
chameleons. Can you solve it? Students who submit solutions (regardless of correctness) and
a pose a question of their own will get access to the other student-posed questions and can
attempt these problems for bonus points.
Turn in solutions to Dr. Skorczewski in Law 204 or by email at tskorczewski@cornellcollege.edu by
November 22. Solutions for only one of the questions or partial solutions will receive credit (and
are encouraged!). For more information about the Problem of the Block see
http://www.cornellcollege.edu/mathematics/problem-of-the-block/index.shtml.
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