Medium Puzzles 

Workings

Hint
The fourth player is the key to this tricky question.

Answer
9 points.

Respectively the scores were 7, 14, 20, 30, 23, 9.

Reasoning
If we label the six players A, B, C, D, E, and F, we know that:

[1]  A + B + C + D + E + F = 103

and from the clues:

   A = B ÷ 2
   B = C – 6
   C = D x 2 ÷ 3
   E = D – A
   F = E – 14

If instead we choose E = A – D, we'd later see that we end up with a negative value for E, which isn't allowed.

Since D is the letter we're missing information for, it's best to find all of the other letters in terms of D.

These steps are left as an exercise (use C in the equation for B, etc), but the result is:

   A = ( D –  9)  ÷ 3
   B = (2D – 18)  ÷ 3
   C = (2D     )  ÷ 3
   D = (3D     )  ÷ 3
   E = (2D +  9)  ÷ 3
   F = (2D – 33)  ÷ 3

Writing it as D = 3D ÷ 3 makes it slightly clearer to see, when adding in the next step.

We can then use these in [1] to find that 12D = 360, so D = 30.

Therefore, F = 9.

Workings

Hint
Remember that each of them told the truth in one of their statements, but lied in the other.

Answer
Billie robbed the bank.

Reasoning
We know that each of them told the truth in one of the statements and lied in the other.

So according to Ashley, as one of the statements is false, it must have been either Drew or Billie.

If it was Drew, then Billie's statements would both be true, which isn't allowed.

Therefore, it was Billie, which agrees with Casey and Drew's statements.

Workings

Hint
Try rewriting each statement so that they are all 'finished before' statements instead.

Answer
Bailey won …

… then Dale, Alex, Chris, and Emery.

Reasoning
By placing the person who finished higher to the left, we have:

Dale finished before Alex (Dale > Alex) Emery finished after Bailey (Bailey > Emery) Alex finished before Chris (Alex > Chris) Emery finished after Dale (Dale > Emery) Bailey finished before Alex (Bailey > Alex) Dale finished after Bailey (Bailey > Dale) Chris finished before Emery (Chris > Emery)
From (1) and (3):

   Dale > Alex > Chris

Adding (7):

   Dale > Alex > Chris > Emery

Adding (6):

   Bailey > Dale > Alex > Chris > Emery

Which is the final placing for all the players, and can be double-checked with the remaining clues.

Workings

Hint
Look at the piece by Bach, and the single.

Answer
Composer   Format  Length
Beethoven  album   6
Holst      single  7
Bach       CD      8
Butler     DAT     9

Reasoning
By (1), the piece by Bach lasts 8 minutes. By (3), the single lasts 7 minutes.
Composer   Format  Length
                   6
           single  7
Bach               8
                   9

By (4), the piece by Butler is on the DAT tape. But, by (2), this can't be the shortest, so it must be 9 minutes long.
Composer   Format  Length
                   6
           single  7
Bach               8
Butler     DAT     9

By (1), the CD can't be the shortest, so must be 8 minutes long.
Composer   Format  Length
                   6
           single  7
Bach       CD      8
Butler     DAT     9

The album must therefore be 6 minutes long, and by (3) doesn't contain any Holst.
Composer   Format  Length
           album   6
Holst      single  7
Bach       CD      8
Butler     DAT     9

Which means that the album was the piece by Beethoven.
Composer   Format  Length
Beethoven  album   6
Holst      single  7
Bach       CD      8
Butler     DAT     9