Random Puzzles 

Workings

Hint
What fraction of the length of the bridge is on the banks?

Answer
5,600 inches.

Reasoning
We know that ¹/₇ + ¹/₈ of the total length is on the banks of the river, and ¹/₇ + ¹/₈ = ¹⁵/₅₆.

So the river width (4,100 inches) is the remaining ⁴¹/₅₆ of the bridge.

Therefore:

   ⁴¹/₅₆ x length = 4100

So:

   length = 4100 x ⁵⁶/₄₁

   length = 5600

As required.

Workings

Hint
The first word is THE.

Answer
The squeaking wheel gets the grease.

Workings

Hint
The answer is a whole number less than 10.

Answer
3.

Reasoning
We can multiply throughout by 12,
    X     X     X     X
    -  -  -  +  -  =  -
    X     2     4     12

to give:

   12 − 6X + 3X = X

        12 − 3X = X

             12 = 4X

              3 = X

As required.

Double-Checking
    3     3     3     3
    -  -  -  +  -  =  -
    3     2     4     12

    1 − 1.5 + 0.75 = 0.25

              0.25 = 0.25, which confirms that 3 is correct.

Workings

Hint
In the word LOG, why might the L have be replaced with 50?

Answer
FO10.

Reasoning
If there is a Roman numeral, it is replaced by its modern equivalent.
   I = 1
   V = 5
   X = 10
   L = 50
   C = 100
   D = 500
   M = 1000

Double-Checking
CLICK = 100 50 1 100 K MILK  = 1000 1 50 K LOG   = 50 O G LIFE  = 50 1 F E ALIVE = A 50 1 5 E FOX   = F O 10