Random Puzzles 

Workings

Hint
How many miles were left at the start of yesterday?

Answer
336 miles.

Reasoning
To work these numbers out, it is perhaps easier to start at the end and work backwards.

Yesterday I travelled ¹/₃ of the distance to leave 21 miles, therefore there were 31.5 miles (=21 ÷ ²/₃) at the start of yesterday.

On day 3 I travelled ³/₄ of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 ÷ ¹/₄) at the start of day 3.

On day 2 I travelled ¹/₂ of the distance to leave 126 miles, therefore there were 252 miles (=126 ÷ ¹/₂) at the start of day 2.

On day 1, I travelled ¹/₄ of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ ³/₄) at the start of day 1.

Double-Checking
On day one, I travelled one quarter of the distance (84, leaving 252).

On day two, I travelled one half of the remaining distance (126, leaving 126).

On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5).

Yesterday I travelled one third of the remaining distance (10.5).

I now have 21 miles left to travel.

Workings

Hint
There are 13 loaves in a baker's dozen.

Answer
Loaves in a dozen baker's dozen.

Reasoning
A baker's dozen is 13, so a dozen baker's dozen is:

   12 x 13 = 156 loaves

There are 15 red balls in snooker, and each of these can be followed by the black ball, and then the colours in order gives:

   15 x (1 + 7) + 2 + 3 + 4 + 5 + 6 + 7 = 147 points

This can rise to 155 if the break follows a foul.

Workings

Hint
Try matching the sock colours to the shoe colours first.

Answer
Baba
   Blue socks and Yellow shoes.
Boba
   Yellow socks and Green shoes.
Bilpo
   Green socks and Red shoes.
Babil
   Red socks and Blue shoes.

Reasoning
We had these colours: Red, Blue, Yellow, Green.
We had these clowns: Baba, Boba, Bilpo, Babil.

Let's match sock colours to shoe colours.

By (1) Red socks went with Blue shoes.

By (6) Green socks went with Red shoes.

By (3) Yellows socks must have gone with Green shoes.

Therefore, Blue socks went with Yellow shoes, which is confirmed with (2).

In summary:
Socks  : Shoes
Red    : Blue
Green  : Red
Yellow : Green
Blue   : Yellow

By (2) Baba had Blue socks and Yellow shoes.

By (4) Boba didn't have Red socks or Red shoes (and Baba had the Blue socks), so must have had Yellow socks and Green shoes.

By (5) Bilpo's shoes were the same colour as Babil's socks. So, we only have Red & Green socks left, and Blue & Red shoes. Therefore, Babil's socks can only have been Red (with Blue shoes).

Leaving Bilpo with Green socks and Red shoes.

Double-Checking
1. The red socks went with the blue shoes [Babil].

2. Baba had yellow shoes but not yellow socks [had Blue].

3. The clown with green shoes did not have blue socks [had Yellow].

4. Boba had neither red shoes nor red socks [had Green shoes and Yellow socks].

5. Bilpo's shoes were the same colour as Babil's socks [Red].

6. The clown with red shoes had green socks [Bilpo].

Workings

Hint
The final word starts with AI.

Answer
Isle becomes aisle.