Random Puzzles 

Workings

Hint
3 raised to the 5^th power is 3 x 3 x 3 x 3 x 3.

Answer
3 raised to 5^th power.

Reasoning
3 raised to the 5^th power = 3 ^ 5 = 3 x 3 x 3 x 3 x 3 = 243

and

5 raised to the 3^rd power = 5 ^ 3 = 5 x 5 x 5 = 125.

Workings

Hint
Start by imaging a sign saying 'BrainBashers Puzzles And Illusions'.

Answer
I commissioned an artist to paint a sign for BrainBashers that said 'BrainBashers Puzzles And Illusions', however, they made a terrible mistake.

The gaps between 'Puzzles' and 'And', and 'And' and 'Illusions' weren't the same, so the sign seemed oddly out of balance.

Workings

Hint
Try to find Drew's boat colours first.

Answer
Alex      Red     + Green
Billie    Green   + Blue
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Reasoning
By (3), Yellow and Blue went together (Combination1: Yellow + Blue).

By (4), Green and Blue went together (Combination2: Green + Blue).

By (2), Billie had Green. By (5), Charlie had Yellow. By (6), Drew had Blue. Giving:
Alex
Billie    Green
Charlie   Yellow
Drew      Blue

By (6), Drew had Blue, but not Green. This can't have been (Combination2: Green + Blue), so must have been (Combination1: Yellow + Blue):
Alex
Billie    Green
Charlie   Yellow
Drew      Blue    + Yellow

By (2), Billie didn't have Red, so Alex and Charlie must have had Red:
Alex      Red
Billie    Green
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Which means that Billie had (Combination2: Green + Blue), and Alex had Green:
Alex      Red     + Green
Billie    Green   + Blue
Charlie   Yellow  + Red
Drew      Blue    + Yellow

Workings

Hint
Start by looking (2).

Answer
Ashley crossed first.

They crossed in the following order (first is on the right):

Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, Ashley.

Reasoning
Starting with (2), we can place Ray, Emery, Logan, and Riley as follows:

   Riley, -, -, Logan, -, Emery, -, Ray, -

(6) tells us that Taylor got on just after Emery, giving us:

   Riley, -, -, Logan, Taylor, Emery, -, Ray, -

(5) tells us that Jessie got on two people before Taylor, giving us:

   Riley, -, -, Logan, Taylor, Emery, Jessie, Ray, -

By (1), Chris got on two people after Logan, giving us:

   Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

And (1) also tells us about Sam, giving:

   Sam, -, Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

We now have a line of 11 people, the missing person is either in front of Ray, or behind Sam.

The only way to place Alex, Quinn, and Billie using (3) and (4) is if the missing person is behind Sam giving:

   -, Sam, -, Riley, Chris, -, Logan, Taylor, Emery, Jessie, Ray, -

And therefore we can now place Alex, Quinn, and Billie as follows:

   Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, -

But who crossed first?

The only person we've not yet found a space for is Ashley. So Ashley crossed first.

   Alex, Sam, Quinn, Riley, Chris, Billie, Logan, Taylor, Emery, Jessie, Ray, Ashley.