[Which Chair you will choose ?]

Got to say, it's __________ that five of us have completely different solutions, and no working in common.

Someone find the right word for me

"interesting". This means the puzzle is so good that it got each one of us to think differently. Thank you for the brain teaser, ujjagrawal.

Although after going through the posts, I am now convinced that bonanova has nailed the answer.

[Which Chair you will choose ?]

The first can only guess it right if the two othes have the same color so:

P_1 = P(ww.bb.bb)+P(bb.ww.ww) = (3/14)^2 * 2 = 9/98 = 9.2%

similarily:

P_2 = P(bb.ww.bb) + P(ww.bb.ww) = P_1 = 9.2%

the third has the following extra advantage:

P_3 = P(bb.bb.ww) + P(ww.ww.bb) + P(bb.ww.bw) + P(ww.bb.bw) = P_1 * 2 = 18.4%

the forth turn (first chair)

P_4 = P(bw.ww.bw) + P(bw.bb.bw) = (3/14) * 2 = 42.9 %

the fifth turn (second chair) or more

P(>5) = 1 - (P_1 + P_2 + P_3 + P_4) = 20.3%

which is lower than the previous seat. therefore, I would choose the first seat since the student on the forth turn has the highest probability.

Please let me know if I missed something.