X
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.
support BrainBashers
??
Puzzle 17
After visiting one of my very old relatives, I travelled home in their old jalopy. The car was old and battered, it had a leak from the petrol tank, and I was stuck in second gear.
This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel.
At the start of the journey, I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour.
Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.
How far was it from my relative's house to my home?
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
?
Puzzle 19
Within the BrainBashers school, the science department has three disciplines.
In total, 280 students study chemistry, 254 students study physics, and 280 students study biology.
In total, 97 students study chemistry and physics, 138 students study physics and biology, and 152 students study chemistry and biology.
73 students study all three disciplines.
Can you determine how many students there are in the science department? The answer is not 814.
Hint
How many students study chemistry and physics, but not biology?
Answer
500 students.
Reasoning
The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.
We know that 73 students study all three disciplines, which allows us to work out the numbers.
97 students study chemistry and physics, so 97 − 73 = 24 study just chemistry and physics.
138 students study physics and biology, so 138 − 73 = 65 study just physics and biology.
152 students study chemistry and biology, so 152 − 73 = 79 study just chemistry and biology.
280 students study chemistry, so 280 − 73 − 24 − 79 = 104 study just chemistry.
254 students study physics, so 254 − 73 − 24 − 65 = 92 study just physics.
280 students study biology, 280 − 73 − 65 − 79 = 63 study just biology.
For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.
?
Puzzle 20
Each empty white square in the grid contains one of the numbers 1, 2, 3, …, 8. Each of the horizontal and vertical equations must be true, and each number must be used exactly once.
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.
