Recent content by cheerful

When I add 3 + 6 + 24 + 696 = 729. This is the total colouring you have suggested. But I don't know how 24 and 696 is computed. ANy ideas?

I got one reply: But how come I don't understand! Do you? The fact that there are 5 hexagons is a red herring. Everything is equiprobable so the problem is reduced to finding the number of matches that are possible. What is tricky is that there are hexagons that match 0, 1, 2, and 5 other...

I think it is still very far. The answer is P(two hexagons with same colors) = 4263/ 3^(6*2) I guess the question is too challenging for the rest to answer. I think you are much better than me.

I found some similar answer but I don't understand how to derive the answer. if I colour my hexagons r(ed), g(reen), b(lue), then obviously the six hexagons (r, r, r, g, g, b) (r, r, g, g, b, r) (r, g, g, b, r, r) etc. are different, but all equivalent. Whereas: (r, r, r, r, r, r) is the only...

I got to submit this homework over the weekend. Able to give me an example for the different ways to compute the symmetry? Thanks

Oops. Its 3^6 ways to color a hexagon. Since I picking two hexagon, I will have 3^6 * 3^6 = 3^(6*2) ways of colors combination. This happens to be denominator. What u mean by radial symmetry?

6^3 ways to color a hexagon. =)

3 different ways to colour each edge. 3^(2*6) is denominator which I think is all the possible combination.

Sure. We can eventually work towards the answer. I am very curious how they arrive 4263 for the numerator. Thanks

The vertices or edges are coloured by three different colours randomly. So we need to find the probability that two hexagons are the same if we picked two of them out of 5 hexagons. They are the same when the sequences of colors are the same with rotations.

There are five hexagons. The edges of each hexagon have been colored with one of three colors randomly. If you pick two hexagons randomly without replacement, what is the probability that they are the same? (Rotation is okay). The total space or denominator is 3^(2×6), therefore we have...