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 58
Below, 10 nine-letter words have been broken into chunks of three letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 words are?
ely rec ant htn fer ort
ent cer por sin lig ian
lio row use rar lib ive
tfo sca ing ing far eth
som dif est dig imp mho
Hint
The first letters of the words are: D, D, F, I, L, L, P, S, S, S.
Answers
dif + fer + ent = different
dig + est + ive = digestive
far + mho + use = farmhouse
imp + ort + ant = important
lib + rar + ian = librarian
lig + htn + ing = lightning
por + tfo + lio = portfolio
sca + rec + row = scarecrow
sin + cer + ely = sincerely
som + eth + ing = something
??
Puzzle 59
I recently gave a new watch to my friend for their birthday.
However, as usual with my presents, it was quite useless as it gains 6 minutes every hour.
I set it using my own accurate clock at midnight, and the watch now shows 8:26am.
I know that it stopped 30 minutes ago, so what is the correct time now?
Hint
This question involves the months of the year in some way.
Answer
4 3 1.
Reasoning
This is the sequence of the length of the name of the month, and the number of days in that month.
7 3 1 = January, which has 7 letters, and 31 days.
8 2 8 = February, which has 8 letters, and 28 days.
5 3 1 = March, which has 5 letters, and 31 days.
5 3 0 = April, which has 5 letters, and 30 days.
3 3 1 = May, which has 3 letters, and 31 days.
4 3 0 = June, which has 4 letters, and 30 days.
Which means the next three digits are:
4 3 1 = July, which has 4 letters, and 31 days.
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