Brain Teasers and Puzzles 

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 first few characters of each word.

Answer
augment.

The first three letters are the same as the first three letters of the months in order.

Workings

Hint
Look at Digit 3 first.

Answer
6394.

Reasoning
Labelling the clues:

Digit 2 is smaller than Digit 4 Digit 4 is two thirds of Digit 1 Digit 1 is two thirds of Digit 3 Digit 3 is three times Digit 2
Using (4), Digit 3 can only be 3, 6 or 9 (as it's 3 x Digit 2).

Therefore, using (4), Digit 2 can only be 1, 2 or 3.

Using (3), Digit 1 can only be 2, 4 or 6 (as it's two thirds of Digit 3).

However, using (2), the only possible value for Digit 1 that we can find two thirds of is 6.

So, using (2), Digit 4 is 4.

So far, we have 6??4.

Using (3), Digit 1 is two thirds of Digit 3, so Digit 3 must be 9.

And, by (4), Digit 2 must be 3.

Giving 6394.