Random Puzzles 

Workings

Hint
Look at the letter positions in the alphabet.

Answer
R.

If you take the alphabetic positions of each letter in a row, the total is always 56.

Double-Checking
Y + G + W + A = 25 +  7 + 23 +  1 = 56
K + L + R + O = 11 + 12 + 18 + 15 = 56
Z + J + P + D = 26 + 10 + 16 +  4 = 56
V + F + T + H = 22 +  6 + 20 +  8 = 56

Workings

Hint
There are no squares of size 5 x 5.

Answer
There are 125 squares without a rook.

Reasoning
61 squares of size 1 x 1
39 squares of size 2 x 2
20 squares of size 3 x 3
 5 squares of size 4 x 4

Giving a total of 61 + 39 + 20 + 5 = 125 squares.

Workings

Hint
There are 3 feet in a yard, 1760 yards in a mile, and 8 furlongs in a mile.

Answer
Square feet in half a square mile.

Reasoning
There are 3 feet in a yard, 1760 yards in a mile, and 8 furlongs in a mile.

A mile is 1760 x 3 = 5280 feet in a mile.

A square mile is 5280 x 5280 = 27878400 square feet.

Therefore, half a square mile = 13,939,200 square feet.

A furlong is 1760 ÷ 8 = 220 yards.

Therefore, a cubic furlong is 220 x 220 x 220 = 10,648,000 cubic yards.

Workings

Hint
The number is less than 20.

Answer
8.

Reasoning
We need a number (N) such that:

2 x N = 14 +  N
             ———
              4

Multiply throughout by 4 to give:

8 x N = 56 + N

So:

7 x N = 56

So N = 8.

Double-Checking
Its double is 16.

Its quarter is 2.

So its double is fourteen more than its quarter.