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Puzzle 293
At a recent visit to the reptile house at the local animal sanctuary, 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.
After the recent BrainBashers drone racing contest, the four contestants were congratulating each other.
Only one drone had the same race number as the position it finished in. Adrian's drone wasn't painted yellow, or blue. Andy's drone beat Avery's drone, whereas Alex's drone beat the drone with race number #1. The drone painted green (Alex's) finished second, and the drone painted blue had race number #4. The drone that had race number #3 was painted red, and beat the drone that finished third. Avery's drone had race number #1.
Can you work out whose drone finished where, its race number, and the colour it was painted?
Hint
Alex's drone finished second, so where did the red drone finish?
Answer Pos Owner # Colour
1 Adrian #3 red
2 Alex #2 green
3 Andy #4 blue
4 Avery #1 yellow
Reasoning
The four colours were: Blue, Green, Red, Yellow.
The four contestants were: Adrian, Alex, Andy, Avery.
By (4), second place was Green, and owned by Alex.
1
2 Alex green
3
4
By (5), Red beat third place, and since Green was second, Red must have been first (and had race number #3).
1 #3 red
2 Alex green
3
4
By (2), Adrian's drone was Red or Green, but we now know that Alex's drone was Green, so Adrian's drone was Red.
1 Adrian #3 red
2 Alex green
3
4
By (3), Andy beat Avery, so they were third and fourth respectively.
1 Adrian #3 red
2 Alex green
3 Andy
4 Avery
By (6), Avery's drone had race number #1.
1 Adrian #3 red
2 Alex green
3 Andy
4 Avery #1
By (1), second place must have had race number #2 (as first place had race number #3, and fourth place had race number #1).
1 Adrian #3 red
2 Alex #2 green
3 Andy
4 Avery #1
Which leaves third place with race number #4, and by (4) was Blue.
1 Adrian #3 red
2 Alex #2 green
3 Andy #4 blue
4 Avery #1
Which leaves fourth place as Yellow.
1 Adrian #3 red
2 Alex #2 green
3 Andy #4 blue
4 Avery #1 yellow
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Puzzle 296
During a recent BrainBashers thinking contest(!), the total number of points scored by the first six players was 103 and every score was above zero.
The first player scored half the points of the second player, who in turn scored 6 points fewer than the third player.
The third player in turn scored two thirds the points of the fourth player.
The fifth player managed to score the same number of points as the difference between the first and fourth player's points (larger − smaller).
Finally, the sixth player scored 14 fewer points than the fifth player.
Can you determine how many points the sixth player managed to score?
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.
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
