stuck at this problem for more than two hours...
It is given that there are at least 1680 ways of painting m different colours into 4 different regions.
Show that m^2 - 3m - 40 >= 0 (Hint: x^2 - 3x + 42 > 0 for all real values of x)
How to show....
have been stuck by this problem for two hours... big headache
Re: stuck at this problem for more than two hours...
Quote:
Originally Posted by
kennysiu 
It is given that there are at least 1680 ways of painting m different colours into 4 different regions.
Show that m^2 - 3m - 40 >= 0 (Hint: x^2 - 3x + 42 > 0 for all real values of x)
What does "at least 1680 ways of painting m different colours into 4 different regions" mean?
Does order matter? Can a colour be repeated? What about rotations.
You have not fully described the question.
Re: stuck at this problem for more than two hours...
Quote:
Originally Posted by
Plato What does "at least 1680 ways of painting m different colours into 4 different regions" mean?
Does order matter? Can a colour be repeated? What about rotations.
You have not fully described the question.
order does matter so it is permutation. Colour cannot be repeated. I don't understand what you mean by rotation. Never encounter such a term.
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Re: stuck at this problem for more than two hours...
Quote:
Originally Posted by
kennysiu order does matter so it is permutation. Colour cannot be repeated. I don't understand what you mean by rotation. Never encounter such a term.
(m-2)(m-3)\ge 1680)
has 
as a solution.
Note (m+5).)
