Brain Teasers and Puzzles 

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
There are no squares of size 5 x 5.

Answer
There are 125 squares without a rook.

Reasoning
61 squares of size 1 x 1
39 squares of size 2 x 2
20 squares of size 3 x 3
 5 squares of size 4 x 4

Giving a total of 61 + 39 + 20 + 5 = 125 squares.

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

Note that it could be E = A − D or E = D − A, but using A − D we'd end up with a negative value for E later, which isn't allowed (so we'd have to try again with D − A anyway).

As we have no information for D, it's best to find all of the other letters in terms of D. These steps are left as an exercise (e.g. use C in the equation for B), 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 things slightly clearer in the next step.

We then use these in [1] to find that:

   (12D − 51) ÷ 3 = 103
         12D − 51 = 309
              12D = 360
                D = 30

Therefore, F = (2D − 33) ÷ 3 = 9.

Workings

Hint
It might be easier to find the S first.

Answer
Start with the P in the 5^th row, 6^th column: