Puzzle 625
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 vs 21/3
Raise each to the power of 30 (since 10 x 3 = 30) to give:
(101/10)30 vs (21/3)30
101/10 x 30 vs 21/3 x 30
103 vs 210
1000 vs 1024
Therefore, the cube root of 2 is larger.
Puzzle 626
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.
Puzzle 627
Where do the biggest potatoes grow?
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Puzzle 628
What are the next five letters in this sequence:
JAJWUTH
TFAPOW
JFDABHC
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Hint
This is a well known nursery rhyme.
Answer
AJCTA.
These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.
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