Puzzle 5
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 6
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 7
How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
How many 2x2 squares are there?
Answer
There are 93 squares without a rook.
Reasoning
There are 60 squares of size 1x1.
There are 33 squares of size 2x2.
Giving a total of 60 + 33 = 93 squares.
Puzzle 8
If...
7/28 of 64 is 16,
and 9/12 of 100 is 75,
and 3/9 of 33 is 11,
what is 5/15 of 45?
Puzzle Copyright © Kevin Stone
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Hint
This puzzle is easier than it first appears.
Answer
15.
Using normal mathematics!
5/15 of 45 = 1/3 of 45 = 15.
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