Random Puzzles 

Workings

Hint
Look at the number of sides of each of the shapes.

Answer
Square.

Reasoning
If we add the shape's sides, the total increases by 8, then 10, then 12, etc (2 more each time).
   triangle (3) + pentagon (5) + square (4) = 12

   square   (4) + hexagon (6) + hexagon (6) + square (4) = 20

   pentagon (5) + hexagon (6) + hexagon (6) + hexagon (6) + square (4) + triangle (3) = 30

Therefore:
   hexagon  (6) + octagon (8) + octagon (8) + octagon (8) + octagon (8) + square (4) = 42

Alternative Reasoning
Square the first shape's sides, and the remaining shapes add up to this number.
   triangle (3 x 3) = pentagon (5) + square (4)

   square   (4 x 4) = hexagon (6) + hexagon (6) + square (4)

   pentagon (5 x 5) = hexagon (6) + hexagon (6) + hexagon (6) + square (4) + triangle (3)

Therefore:
   hexagon  (6 x 6) = octagon (8) + octagon (8) + octagon (8) + octagon (8) + square (4)

Workings

Hint
Start by counting the letters you're given.

Answers
This sentence contains sixty-seven letters, one hyphen, two commas and a full stop. Interestingly, this sentence contains eighty-nine letters, one hyphen, three commas and the final full stop. Finally, this sentence contains seventy-nine letters, one hyphen, three commas and one full stop.

Workings

Hint
Look at the first letters.

Answer
November.

This is the next month in alphabetical order:

April, August, December, February, January, July, June, March, May, November, October, September.

Workings

Hint
Try starting with the cube root of the number.

Answer
42, 44, and 46.

Reasoning
As we require 3 numbers that are multiplied together, we can start with the cube root of 85,008 ≈ 43.97.

We can now check that 44 divides 85,008 exactly: 85,008 ÷ 44 = 1,932, which means that 44 is likely to be one of the numbers.

And as we know that we need consecutive even numbers, we soon find 42 and 46 as the remaining numbers.

Double-Checking
42 x 44 x 46 = 85,008.