The final of the BrainBashers triathlon was a close run thing.
The whole tournament was decided on the last two sections, cycling and the road race.
Alex didn't win either section. The person who won the cycling came third in the road race. Alex beat Charlie in cycling, but was beaten by Charlie in the road race. Charlie was last in neither section. Drew won the road race, but was beaten by Billie in the cycling.
Can you work out who came where in each section?
Hint
In the road race, where could Charlie have finished?
Answer
Cycling : Billie > Alex > Charlie > Drew
Road race : Drew > Charlie > Billie > Alex
Road Race
In the road race, where could Charlie have finished?
By (4), he wasn't last. By (5), he wasn't first.
By (2), if Charlie was third, then he would have won the cycling, but by (3) Alex beat Charlie in the cycling, so Charlie can't have won the cycling.
So Charlie must have finished in second place.
By (5), Drew was first.
By (1), Alex didn't win the cycling, so by (2) he didn't come third in the road race. Therefore, Alex came last.
Leaving Billie in third place.
Road race : Drew > Charlie > Billie > Alex
Cycling
By (2), Billie won.
By (4), Charlie wasn't last.
By (3), Alex beat Charlie. So Alex finished in second place, with Charlie in third place.
Leaving Drew in last place.
Cycling : Billie > Alex > Charlie > Drew
??
Puzzle 42
Farmer Stone is quite an eccentric dairy farmer.
He originally had a total of 54 gallons of milk in three churns, and he wanted to make sure each churn contained 18 gallons of milk.
In order to do this, he did the following:
First, he poured 1/4 of the first churn into the second churn. He then poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn.
How many gallons did each churn contain before Farmer Stone started pouring?
Hint
Try working backwards with each churn containing 18 gallons.
Answer
12, 33, and 9 gallons respectively for churns 1, 2, and 3.
Reasoning
Working backwards, at the end after Pour 3, the churns (C1, C2, C3) contained:
C1 C2 C3
————————————
18 18 18 after Pour 3
Pour3 was 1/3 of C3 into C1, the remaining 2/3 has to be the 18 gallons left in C3 after the pour, which means that 1/3 is 9 gallons. So 9 gallons was poured from C3 into C1. Before Pour3, C1 must have contained 9 gallons, and C3 contained 27 gallons.
C1 C2 C3
————————————
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour2 was 1/2 of C2 into C3, the remaining 1/2 has to be the 18 gallons left in C2 after the pour, which means that 1/2 is 18 gallons. So 18 gallons was poured from C2 into C3. Before Pour2, C2 must have contained 36 gallons, and C3 contained 9 gallons.
C1 C2 C3
————————————
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour1 was 1/4 of C1 into C2, the remaining 3/4 has to be the 9 gallons left in C1 after the pour, which means that 1/4 is 3 gallons. So 3 gallons was poured from C1 into C2. Before Pour2, C1 must have contained 12 gallons, and C2 contained 33 gallons.
C1 C2 C3
————————————
12 33 9 at the start
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
??
Puzzle 43
The BrainBashers Speed Skating championship was recently completed, however, the computer storing the results suffered from a power cut!
Using the following snippets of information, can you work out who finished where, their ages (18, 21, 24, and 28), and the colour they wore?
The youngest, who didn't wear blue, won the championship. Jesse was three years younger than the person who wore red. Kelly performed well to finish in second place. Logan wore green, and Max was the oldest competitor. The person who wore yellow was younger than Kelly. The person who came last was 21.
Answer
#1 Logan Green 18
#2 Kelly Red 24
#3 Max Blue 28
#4 Jesse Yellow 21
Reasoning
By (1), the 18-year-old won the championship.
By (3), Kelly finished second.
By (6), the person who came last was 21.
#1 18
#2 Kelly
#3
#4 21
By (4), Max was the oldest competitor at 28, and can only have finished third. Which means that Kelly must have been 24.
#1 18
#2 Kelly 24
#3 Max 28
#4 21
By (2), the person who wore Red can only be 21 or 24, so Max can't have worn Red. Max didn't wear Green (4), and didn't wear Yellow (5), so Max must have worn Blue.
#1 18
#2 Kelly 24
#3 Max Blue 28
#4 21
By (5), Kelly didn't wear Yellow, and by (4) didn't wear Green, so must have worn Red.
#1 18
#2 Kelly Red 24
#3 Max Blue 28
#4 21
By (2), Jesse was 21. Which means that Logan was 18.
#1 Logan 18
#2 Kelly Red 24
#3 Max Blue 28
#4 Jesse 21
By (4), Logan wore Green. Which means that Jesse wore Yellow.
#1 Logan Green 18
#2 Kelly Red 24
#3 Max Blue 28
#4 Jesse Yellow 21
??
Puzzle 44
Last week I decided to cycle to my Grandparents's house.
On the 1st day, I cycled half of the distance.
On the 2nd day, I cycled one half of the remaining distance.
On the 3rd day, I cycled three quarters of the remaining distance.
On the 4th day, I cycled 10 miles.
On the 5th day, I cycled two thirds of the remaining distance.
On Day 5, I started with 15 miles (as I cycled two thirds, leaving 5 miles).
On Day 4, I started with 25 miles (as I cycled 10 miles).
On Day 3, I started with 100 miles (as I cycled three quarters, leaving 25 miles).
On Day 2, I started with 200 miles (as I cycled half, leaving 100 miles).
On Day 1, I started with 400 miles (as I cycled half, leaving 200 miles).
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