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Puzzle 85
Take away eight of the sticks below, and leave one stick behind.
There are no hidden sticks.
Note: this puzzle is not interactive, and cannot be clicked.
Answer
If you look carefully, you will see that there are actually two sticks under the other seven, so you can take away eight sticks and still leave one behind.
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Puzzle 86
Some months have 30 days, some have 31, but how many have 28 days?
Start in the bottom left corner and move either up or right, one square at a time, using the numbers and the mathematical signs along the way. What is the largest total you can make?
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2
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4
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2
2
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2
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2
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1
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3
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3
2
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3
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1
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1
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3
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2
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3
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2
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Note: this puzzle is not interactive, and the numbers cannot be clicked.
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
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.
