Random Puzzles 

Workings

Hint
Think of the pages from 1-9, and then 10-99.

Answers
There are 147 pages. The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.

For pages 10-99, there are 90 pages, which is 180 digits.

This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.

Taking us to 9 + 90 + 48 = 147 pages in total.

Answer #2
From page 1 to 147 we have 15 pages that end in 3:

   3, 13, 23, …, 143

We also have the ten pages that start with 30:

   30, 31, 32, …, 39

Plus the ten pages that start with 130:

   130, 131, 132, …, 139

For a total of 15 + 10 + 10 = 35 number 3's.

Workings

Hint
Could Alex Ambleton have won?

Answer
Taylor Tripton won with Midday Night.

Reasoning
Before we begin the reasoning, let's look at the hint: 'Could Alex Ambleton have won?'. There are three horses in the puzzle, and Alex Ambleton is stated to have won with all three of them. We know that none of the statements were fully true, so Alex couldn't have won otherwise one of the statements would have been fully true.

However, we don't need the hint to solve the puzzle.

By grouping the clues together, we have:

1. Frankie Flanton won with Morning Sunset.
2. Frankie Flanton won with Evening Sunrise.
3. Frankie Flanton won with Evening Sunrise.

4. Sam Spinton won with Midday Night.
5. Sam Spinton won with Midday Night.
6. Sam Spinton won with Midday Night.
7. Sam Spinton won with Morning Sunset.

8. Taylor Tripton won with Morning Sunset.
9. Taylor Tripton won with Evening Sunrise.

10. Alex Ambleton won with Midday Night.
11. Alex Ambleton won with Morning Sunset.
12. Alex Ambleton won with Evening Sunrise.

We know that none of these statements were fully true, so, we know that (for example) it wasn't Frankie Flanton with Morning Sunset.

We can create a grid of all the possibilities and place an X where we know that it can't have been that combination:

We now have an X for all but 3 possibilities, and we know that exactly 6 of the clues must be half true.

So …

… if it was Frankie Flanton with Midday Night then exactly 7 clues would be half true (clues 1, 2, 3, 4, 5, 6, 10).

… if it was Sam Spinton with Evening Sunrise then exactly 8 clues would be half true (clues 4, 5, 6, 7, 2, 3, 9, 12).

… if it was Taylor Tripton with Midday Night then exactly 6 clues would be half true (clues 8, 9, 4, 5, 6, 10) – so this must be the correct answer.

Workings

Hint
Consonants and vowels (AEIOU) are each worth something.

Answer
12 miles away.

Consonants are worth 2 and vowels (AEIOU) are worth 3.

Double-Checking
York
   3C + 1V = 3 x 2 + 3 = 9
London
   4C + 2V = 4 x 2 + 2 x 3 = 14
Manchester
   7C + 3V = 7 x 2 + 3 x 3 = 23
Leeds
   3C + 2V = 3 x 2 + 2 x 3 = 12

Workings

Hint
A little logic is required.

Answer
# Name
   Wore  Deck Colour

1 DJ Skinf Lint
   2     red

2 DJ Park'n Ride
   3     yellow

3 DJ Slam Dunk
   1     green

4 DJ Jam Jar
   4     blue