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Hint: The fourth player is the key to this tricky question.
Answer: 9 points.
Respectively the scores were 7, 14, 20, 30, 23, 9.
If the six player were A, B, C, D, E and F we know that:
A + B + C + D + E + F = 103 [1]
and
A = B ÷ 2
B = C  6
C = D x 2 ÷ 3
E = D  A (see note at end)
F = E  14
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, but the result is:
A = (2D  18) ÷ 6
B = (2D  18) ÷ 3
C = 2D ÷ 3
E = (2D + 9) ÷ 3
F = (2D  33) ÷ 3
We can then use these all in [1] to find that D = 30. Which allows us to find F = 9.
Small note: if we chose E = A  D (instead of E = D  A) we'd end up with a negative value for E, which isn't allowed.
Puzzle 31
The results for a recent Chess tournament between five close rivals is described below:
Dave finished before Adam.
Eileen finished after Betty.
Adam finished before Charles.
Eileen finished after Dave.
Betty finished before Adam.
Dave finished after Betty.
Charles finished before Eileen.
Hint: Try writing each statement as 'finished before'.
Answer: Betty won, then Dave, Adam, Charles and Eileen.
By placing the person who finished higher to the left we have:
1. Dave finished before Adam Dave > Adam 2. Eileen finished after Betty Betty > Eileen 3. Adam finished before Charles Adam > Charles 4. Eileen finished after Dave Dave > Eileen 5. Betty finished before Adam Betty > Adam 6. Dave finished after Betty Betty > Dave 7. Charles finished before Eileen Charles > Eileen
From 1 and 3:
Dave > Adam > Charles
Adding 7:
Dave > Adam > Charles > Eileen
Adding 6:
Betty > Dave > Adam > Charles > Eileen
Which is the final placing for all of the players, and can be double checked with the remaining clues.
Puzzle 32
Below are ten words, from each word, remove a single letter and rearrange the remaining letters to find ten new words which are related to each other.
ENERGY
DOORMAN
CLEAREST
WEIGHT
OUTLIVE
EMBARK
CALMER
SOLEMN
VOIDING
ARCHERY
ENERGY  Y = GREEN
DOORMAN  D = MAROON
CLEAREST  E = SCARLET
WEIGHT  G = WHITE
OUTLIVE  U = VIOLET
EMBARK  K = AMBER
CALMER  L = CREAM
SOLEMN  S = LEMON
VOIDING  V = INDIGO
ARCHERY  A = CHERRY
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