Medium Puzzles 

Workings

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

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

For pages 10 to 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
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