Thread: 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

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.

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.

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.

has as a solution.

Note