Puzzle 281
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 282
Here are some less well known proverbs. What is the missing word in each?
Loyalty is worth more than {?}.
He that cannot pay in {?} must pay in person.
Shameful {?} is worse than shameful eating.
Don't say {?} until you are asked.
Payment in advance is {?} payment.
Puzzle Copyright © Kevin Stone
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Answer
Loyalty is worth more than money.
He that cannot pay in purse must pay in person.
Shameful leaving is worse than shameful eating.
Don't say no until you are asked.
Payment in advance is evil payment.
Puzzle 283
Which is larger …
… the tenth root of 10, or the cube root of 2?
Puzzle Copyright © Kevin Stone
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Hint
You don't need to use a calculator.
Answer
Cube root of 2.
Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.
But, if you've not got your calculator handy …
We have:
101/10 or 21/3
Raise each to the power of 30 (since 10 x 3 = 30) to give:
(101/10)30 or (21/3)30
101/10 x 30 or 21/3 x 30
103 or 210
1000 or 1024
Therefore, the cube root of 2 is larger.
Puzzle 284
What number comes next in this sequence:
3 3 5 4 4 3 5 {?}
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Hint
This is a very common sequence.
Answer
5.
The numbers represent the number of letters of the words ONE, TWO, THREE, etc. Therefore the answer is the number of letters in the word EIGHT.
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