ElectricPavlov

Wow...this is really twisting the visualizations in my mind around!

I believe YOU have it CORRECT !     Well done...

I recounted....(yes, yet again)

two opposite faces   18

two faces with  7       14

two faces with  5        10       for a total of 42 painted little cubes!

125-42 = 83 without paint ....as you found!     Yikes...My batting average today is very low!

Zero time is arbitrary......  say you are running for a while and cross a line.....we can call that time zero...you were running before you crossed that line....you were running at time t = -2    and time = -10 etc.

Or consider rocket launches where they say t-minus 4    t-3   t-2  t-1   ignition !   time zero is ignition in this case ....but things were going on during t-3  t-2  t = -1   etc

....and I would have 96 typos if I tried to type an answer that long tertre.....strong work!

You may be correct.....I am assuming you can position the democrats and repub blocks 10 different ways araound the table....you are assuming there is only one way (it IS a round table after all).

That is why my answer is 10 times bigger than yours.....I hope someone who KNOWS the answer can chime in, but here is my reasoning (which may be incorrect for a ROUND table with no reference point.....but ok for a rectangular table....just dont know)

  I suspect YOUR answer is correct as far as ORDER of the people go as you go around the table....but if the table is referenced as in my diagram to North...or the door of the room or the window in the room etc, then does the answer change?

  What would happen if there were 11 chairs? (I think THAT would make my answer more correct)

Learning !

See above edited answer.....   Thanx Tertre ! 

Another wrong answer!   See discussion.....and Tertre's CORRECT answer below.

(Geez)

Good work!

Yes...... that is what I would do.     $/(can/week)  is the units   (don't forget units in your math answers.....technically, w/out units your answer is incorrect!)      

Thanx for your help GA !   I am still getting 're-acquainted' with this stuff.......can you backcheck my answer for the 5 Repubs and 5 Dems sitting around a table???    G'Day ...     ~EP

As a block of 5 and 5 there are 10 ways to sit around the table   10.

  Now , WITHIN  EACH block there is 5! ways to sit

     AND for EACH of the 5! ways to sit in one block there are 5! ways to sit in the OTHER block....

so   10 x 5! x 5! = 144,000 ways

      (I am still learning this stuff like you.....as GA can attest!  So this answer may be incorrect!)     ~EP

GA.....I'm still confused I guess.  The knot in the bracelet makes it essentially 'knot' (pun) a circle but a straight line configuration......the beads cannot rotate...they are in a straight line.    So I (think) my naswer is correct, not coincidental.  Maybe we are viewing the question differently in our minds' eyes?