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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. QED.
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 2
During the recent BrainBashers football competition, 5 schools were competing.
Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost.
Here are the final points after all of the matches:
Since there were 5 teams in the league there were a total of 10 possible games (either way around):
Longton vs Fenton
Longton vs Blurton
Longton vs Hulton
Longton vs Fulton
Fenton vs Blurton
Fenton vs Hulton
Fenton vs Fulton
Blurton vs Hulton
Blurton vs Fulton
Hulton vs Fulton
Since each game distributed 2 points to the two teams there were a total of 20 points available to the league.
The results shown add to 17, leaving the remaining 3 to Fulton. QED.
Puzzle 3
At a recent visit to the reptile house at the local zoo, I counted a total of 27 heads and 70 feet.
I was counting snakes, lizards and people and I know that there were exactly twice as many lizards as people.
Day 4: travelled 3/4 leaving 5 miles, which means that 5 miles is 1/4, so 20 miles were left at the start of Day 4.
Day 3: travelled 2/3 leaving 20 miles, which means that 20 miles is 1/3, so 60 miles were left at the start of Day 3.
Day 2: travelled 1/2 leaving 60 miles, which means that 60 miles is 1/2, so 120 miles were left at the start of Day 2.
Day 1: travelled 1/3 leaving 120 miles, which means that 120 miles is 2/3, so 180 miles were left at the start of Day 1.
Of the 180 miles overall, 175 were covered in the 4 days. QED.
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