Puzzle 13
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?
Puzzle Copyright © Kevin Stone
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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 14
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.
Puzzle Copyright © Kevin Stone
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Hint
Where did Max finish?
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 15
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 the final day, I cycled the remaining 5 miles.
How far is it to my Grandparent's house?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
400 miles.
Reasoning
Working backwards:
On the final day I cycled the remaining 5 miles
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).
Puzzle 16
Bog Snorkelling - Logic Puzzles
Four friends were competing in the internationally renowned BrainBashers Bog Snorkelling competition.
As usual, the judges were a little careless and once again, they managed to lose the results.
Luckily, a number of spectators were able to remember the following snippets of information:
Only one person wore the same number as the position they finished.
Gary, who didn't wear green, beat Barry.
Larry beat the person who wore yellow.
The person who wore number 3, wore green.
The person who wore number 2 finished first, whereas Harry came last.
The person who finished second wore green, Barry wore yellow, and the person wearing red beat the person wearing blue.
Can you work out who finished where, and the number and colour they wore?
Puzzle Copyright © Kevin Stone
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Hint
Start by looking at clue (5), and then at the first part of clue (6).
Answer
# Name Wore Colour
1 Gary 2 red
2 Larry 3 green
3 Barry 1 yellow
4 Harry 4 blue
Reasoning
By (5), the winner wore #2, and Harry finished last:
# Name Wore Colour
1 2
2
3
4 Harry
By (6), the person who finished second wore green, and by (4), wore #3:
# Name Wore Colour
1 2
2 3 green
3
4 Harry
By (1), only the person in last place could have worn the same number as the position they finished:
# Name Wore Colour
1 2
2 3 green
3 1
4 Harry 4
By (3), Gary didn't wear green (so can't have finished second) and beat Barry (so can't have finished third), which means that he must have finished first.
# Name Wore Colour
1 Gary 2
2 3 green
3 1
4 Harry 4
By (6), Barry wore yellow, so must have finished third:
# Name Wore Colour
1 Gary 2
2 3 green
3 Barry 1 yellow
4 Harry 4
By (6) the person wearing red beat the person wearing blue, giving:
# Name Wore Colour
1 Gary 2 red
2 Larry 3 green
3 Barry 1 yellow
4 Harry 4 blue
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