Random Puzzles 

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.

Workings

Hint
Think of the phrase 'my bucket and spade'.

Answer
In the phrase 'my bucket and your spade', the gap between 'my' and 'and' is the same as the gap between 'and' and 'spade', namely one word.

Indeed, this logic can be continued to give the following sentence. In the first sentence the gap between 'and and' and 'and and' is seven words, et cetera.

Workings

Hint
Which digit is removed each time?

Answer
97.

Reasoning
The lowest digit is removed each time.

Workings

Hint
Look at Digit 3 first.

Answer
6394.

Reasoning
Labelling the clues:

Digit 2 is smaller than Digit 4 Digit 4 is two thirds of Digit 1 Digit 1 is two thirds of Digit 3 Digit 3 is three times Digit 2
By (3), Digit 3 is divisible by 3:

   Digit 3 = 3, 6, 9

By (3), Digit 1 is two thirds of Digit 3:

   Digit 1 = 2, 4, 6.

But, by (2), Digit 1 is divisible by 3:

   Digit 1 = 6, and Digit 3 = 9.

By (4), Digit 3 is three times Digit 2:

   Digit 2 = 3.

By (2), Digit 4 is two thirds of Digit 1:

   Digit 4 = 4.