Random Puzzles 

Workings

Hint
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, …

Answer
71.

The first twenty prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

Workings

Hint
Which painting won, and who came first?

Answer
#  Name     Artist
1  Alex     Monet
2  Emery    Constable
3  Glen     Van Gogh
4  Drew     Taylor
Reasoning
The four entrants were: Alex, Drew, Emery, Glen.
The four artists were: Constable, Monet, Taylor, Van Gogh.

By (2), the Monet came first.
   1           Monet
   2 
   3 
   4 

By (3), Glen came third.
   1           Monet
   2
   3  Glen
   4

By (1), the Constable can't have been last, so must have been second (as Emery painted it, and not Glen).
   1           Monet
   2           Constable
   3  Glen
   4

The Taylor was either third or fourth, either way, by (4) Alex must have won.
   1  Alex     Monet
   2           Constable
   3  Glen
   4

By (4), the Van Gogh came third, leaving Drew in last place.
   1  Alex     Monet
   2           Constable
   3  Glen     Van Gogh
   4  Drew

Leaving Emery in second place, and the Taylor in last place.
   1  Alex     Monet
   2  Emery    Constable
   3  Glen     Van Gogh
   4  Drew     Taylor

Workings

Hint

Answer
Fred, Darren, Nick.

Workings

Hint

Answer
Gravity.