Medium 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
The first letters of the words are: B, C, D, F, J, W.

Answers
Beaver, coyote, donkey, ferret, jaguar, walrus.
EAR + BVE = BEAVER

CYO + OTE = COYOTE

OKY + DNE = DONKEY

RRT + FEE = FERRET

AGU + JAR = JAGUAR

WLS + ARU = WALRUS

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.