[Calc-quickie]

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 C^(3/2)  ? Unless there some trick involved.

 

[Jelly beans join the clean plate club]

I have a doubt to confirm.

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Lets say we were transferring from plate B to A . When you said fuller plate , do you mean that the (no of beans on  A)<( no of beans on B)  , or do you mean (no of beans on A)<=(no of beans on B)? My final answer will depend on this condition.

 

[Adapting a classic crossing puzzle]

Ok , NOW  I got it ,

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8 mins  is the fastest
lets consider fast rower as r  , and slower as s ,    and   | |   be the bridge 
sssrr  |  |                                     0 min
 sss     |  |    rr                             1 min
 sssr   |  |   r                                2 min
       r    |  |    sssr                        6 min
      rr   |  |   sss                           7 min 
            |  |   sssrr                        8 min

 

[Adapting a classic crossing puzzle]

After going through a few ways to cross the river , shortest time is 

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9 mins

 

[Cubicle Stack]

I think I got it ....

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Using a rubics cube     , and using rotational symmetry to simplify counting I get,

C- core   ,    M - middle or face ,    E - edge,     R-  as in corner.

CM- 1         MM -2         EE - 5   
CE  -1         ME  -3         ER  -4
CR -1          MR -2          RR -3
       3    +            7      +       12        =    22 ways  

 

[Cubicle Stack]

Not sure if my method is the right way to do it...

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Now , we can only choose a core , corner , edge or the middle piece from all the pieces.
I made a table where I took 1 piece , and then check the no of ways I can take the second piece.
                                                  corner                edge                 center               core
                       core                       1                          1                        1                        X                 = 3 ways
                       corner                  3                           3                       2                         X                 =8 ways
                       edge                     X                           4                       3                         X                 = 7 ways
                       center                  X                           X                       2                         X            =    2 ways
X is marked for spots that are already counted .
So , total distinct no of shapes =  3+8+7+2 = 20 ways

 

[What am I ?]

 plasmid , your second answer was right !!

[What am I ?]

Well that would have been right , but then almost every "what am I question" can be answered with that .  The following is a clue of sort....

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It is a living thing (technically) that exists and everyone knows about.

 

[What am I ?]

I have legs , ears , eyes , leaves , tails , wings , and trunks . What am I ?

[Russian Roulette]

After the chamber is spun , the bullet can only occupy 6 positions .

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And in going through all the positions :

1. bullet in 1st position -- 1st guy loses
2. bullet in 2nd position -- 2nd guy loses
3. bullet in 3rd position -- 3rd guy loses 
4. bullet in 4th position -- 4th guy loses
5. bullet in 5th position -- 5th guy loses 
6. bullet in 6th position -- 1st guy loses

And since these are all the possibilities that can happen and there are no other possible outcomes , 
the position at 2nd , 3rd , 4th and 5th are the safest with 1/6 chance of lossing .
This is pretty much it I guess.... tell me if I am wrong.

 

 

[Segment a segment]

One more thing , does this problem have a solution?
And is the line and line segment given intersecting , parallel or just inclined and not intersecting?