Medium Puzzles 

Workings

Hint
The first word begins with T.

Answer
Too many cooks spoil the broth.

Reasoning
The saying has been broken down into blocks of 4, the last block has been filled with dummy letters. Each block has then been reversed.

Double-Checking
Start with:
   TOO MANY COOKS SPOIL THE BROTH

Group together:
   TOOMANYCOOKSSPOILTHEBROTH

Split into groups of 4 letters:
   TOOM ANYC OOKS SPOI LTHE BROT H

Add 3 random characters:
   TOOM ANYC OOKS SPOI LTHE BROT HBCY

Reverse each group of 4 letters:
   MOOT CYNA SKOO IOPS EHTL TORB YCBH

Workings

Hint
What can digits 4 and 5 be?

Answer
71842.

Reasoning
The number can be represented as:

   - - - - -

By (5), Digit 5 is half of Digit 4, so we have four possibilities:

   - - - 2 1
   - - - 4 2
   - - - 6 3
   - - - 8 4

By (4), Digit 1 is higher than the sum of Digit 4 and Digit 5, so we can eliminate two possibilities, leaving:

   - - - 2 1
   - - - 4 2

By (7), Digit 5 is between Digit 2 and Digit 1, so we can eliminate - - - 2 1, leaving:

   - - - 4 2

By (4), Digit 1 must be higher than the sum of Digit 4 and Digit 5, so we have three possibilities:

   7 - - 4 2
   8 - - 4 2
   9 - - 4 2

By (6), Digit 1 is 1 smaller than Digit 3 we can eliminate 9 - - 4 2, and fill in Digit 3, leaving:

   7 - 8 4 2
   8 - 9 4 2

By (3), Digit 2 is the lowest digit, and must be 1:

   7 1 8 4 2
   8 1 9 4 2

By (1), the only possibility is:

   7 1 8 4 2

Workings

Hint
Who came first?

Answer
Happy Hippo
 Eagle Wings
  Chippy Flippers
   Arlington Wonderers
    Foxtrot Foxes
     The Mad Hatters
      Bright Moon
       Derby Surefires

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.

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.