Random Puzzles 

Workings

Hint
How many 2 x 2 squares are there?

Answer
There are 128 squares without a rook.

Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are  6 squares of size 4 x 4.
There is   1 square  of size 5 x 5.

Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.

Workings

Hint
How many watch minutes pass in a real hour?

Answer
8:10am.

Reasoning
The watch now shows 8:26am, so we know that 8 x 60 + 26 = 506 watch minutes have passed.

Since the watch is gaining 6 minutes every hour, for every real hour that has passed, the watch will show 66 minutes.

So, 506 ÷ 66 ≈ 7.666 real hours have passed.

This equals 460 minutes, which is 7 hours and 40 minutes = 7:40am.

The watch stopped 30 minutes ago, therefore the time must now be 8:10am.

Workings

Hint
Think laterally.

Answer
Simply rotate it 180 degrees!

Workings

Hint
A little bit of algebra might help.

Answer
I asked for 7 feet, 4 inches and Alex brought me 4 feet, 7 inches.

Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:

   ⁵/₈ x (12 x A + B) = (12 x B + A)

Simplifying gives:

   A = ⁹¹/₅₂ x B

As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.

B = 4 is the only possible value, which means that A = 7.

So I originally asked for 7 feet, 4 inches.

Double-Checking
I received 4 feet, 7 inches = 55 inches.

I asked for 7 feet, 4 inches = 88 inches, and 88 x ⁵/₈ = 55.