Random Puzzles 

Workings

Hint
Mary's name is Dancer.

Answer
Louise Archer will make the chocolate cake.
Julie Bowness will make the coffee cake.
Kay Cook will make the plain cake.
Mary Dancer will make the vanilla cake.

Workings

Hint
Do the words make sense when read another way?

Answer
Nwod.

Opposites reversed:
   big and small
   open and closed
   up and down.

Workings

Hint
How many different ways could the sign be placed back?

Answer
I simply pointed Chesterton back the way I had come and this left the sign in its correct orientation.

Workings

Hint
Look at the first and third columns first.

Answer
The missing sum is 40.
Circle   = 12
Star     = 3
Square   = 7
Triangle = 9

Reasoning
Looking at Column 1 and Column 3 we have:

[1]   Square + Star + Circle + Square = 29
[2]   Square + Square + Triangle + Star = 26

If we subtract [1] − [2] we get:

[3]   Circle − Triangle = 3

And Row 3 is:

[4]   Circle + Circle + Triangle + Circle = 45

If we add [3] + [4] we get:

Circle + Circle + Circle + Circle = 48

So, Circle = 12.

Using [3] we find that Triangle = 9.

Using Column 2 we find that Star = 3.

Using Row 1 we find that Square = 7.

Double-Checking
The rows add to: 35 + 26 + 45 + 25 = 131.

The columns add to: 29 + 36 + 26 + 40 = 131.

The rows and columns must add to the same number, so this could have been used a shortcut to the missing sum.

In total, there are:
   5 Squares   = 5 x 7  = 35
   5 Circles   = 5 x 12 = 60
   3 Stars     = 3 x 3  =  9
   3 Triangles = 3 x 9  = 27

Which is also a total of 131.

So all of the totals are the same, as expected.