Puzzle 1
Practical Pat was asked to cut a 99 foot rope into three smaller, equal length ropes.
However, as usual, Pat couldn't find the measuring tape, so a guess took place!
When the tape was finally found (it was under a hat), Pat discovered that:
the second piece of rope was twice as long as the first piece, minus 35 feet
the third piece of rope was half the length of the first, plus 15 feet
How long were each of the pieces of rope?
Puzzle Copyright © Kevin Stone
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Hint
Only one of the ropes was exactly 33 feet.
Answer
First = 34 feet.
Second = 33 feet.
Third = 32 feet.
Reasoning
This question can be solved using algebra. If we call the length of the first rope A, we have:
Rope 1 = A
Rope 2 = 2 x A − 35
Rope 3 = 0.5 x A + 15
The three ropes add to 99 feet:
99 = Rope 1 + Rope 2 + Rope 3
99 = A + (2 x A − 35) + (0.5 x A + 15)
99 = 3.5 x A − 20
119 = 3.5 x A
34 = A
Giving:
Rope 1 = 34 feet
Rope 2 = 2 x 34 − 35 = 68 − 35 = 33 feet
Rope 3 = 1 ÷ 2 x A + 15 = 1 ÷ 2 x 34 + 15 = 17 + 15 = 32 feet
Double-Checking
Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99
Puzzle 2
After a day picking strawberries, I ended up with a full basket, which is always nice.
I ate 5, and then gave Alex half of the remaining.
I ate another 3, and then gave Billie one third of the remaining.
I ate another 6, and then gave Charlie two thirds of the remaining.
I now had 34 strawberries left. How many did I start with?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
335 strawberries.
Reasoning
Working backwards …
I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.
I ate 6 myself, so I had 108 before I ate those.
I had 108 strawberries, so I had 162 before giving Billie one third.
I ate 3 myself, so I had 165 before I ate those.
I had 165 strawberries, so I had 330 before giving Alex one half.
Ate 5 myself, so I had 335 before I ate those.
Therefore, I started with 335 strawberries.
Double-Checking
I started with 335.
I ate 5, leaving 330.
I gave Alex half (165), leaving 165.
I ate 3, leaving 162.
I gave Billie one third (54), leaving 108.
I ate 6, leaving 102.
I gave Charlie two thirds (68), leaving 34.
Puzzle 3
At the recent BrainBashers code-breaking convention, Billie Brisk won the speed contest.
The following sentence was deciphered in a record time of 123 seconds.
What was the well-known saying, and how has it been encrypted?
MOOT CYNA SKOO IOPS EHTL TORB YCBH
Puzzle Copyright © Kevin Stone
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Hint
The first word begins with T.
Answer
Too many cooks spoil the broth.
Reasoning
The saying has been broken down into blocks of 4, the last block has been filled with dummy letters. Each block has then been reversed.
Double-Checking
Start with:
TOO MANY COOKS SPOIL THE BROTH
Group together:
TOOMANYCOOKSSPOILTHEBROTH
Split into groups of 4 letters:
TOOM ANYC OOKS SPOI LTHE BROT H
Add 3 random characters:
TOOM ANYC OOKS SPOI LTHE BROT HBCY
Reverse each group of 4 letters:
MOOT CYNA SKOO IOPS EHTL TORB YCBH
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