Puzzle 697
Can you find three consecutive prime numbers …
… that equal 409,457 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
The cube root of the given number is a good starting point.
Answer
71, 73, 79.
Reasoning
The cube root of 409,457 is around 74.
The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.
Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.
Puzzle 698
Here is a well known proverb with the consonants removed. What is the proverb.
A -i-- i- --e -a-- i- -o--- --o i- --e -u--.
Puzzle Copyright © Kevin Stone
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Hint
The seventh word is WORTH.
Answer
A bird in the hand is worth two in the bush.
Puzzle 699
Using a 3 gallon container and a 7 gallon container (along with a water source and drain) …
… can you measure exactly 5 gallons in the fewest steps?
Puzzle Copyright © Kevin Stone
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Hint
Start by filling the 7 gallon container.
Answer
Here are the contents of the containers after each stage:
A B
0 7 fill B
3 4 fill A from B
0 4 empty A
3 1 fill A from B
0 1 empty A
1 0 fill A from B
1 7 fill B
3 5 fill A from B
This leaves 5 gallons in container B after 8 steps.
Puzzle 700
What number comes next in this sequence:
7 8 5 5 3 4 4 {?}
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Hint
The answer involves months of the year.
Answer
6.
The number of letters each month has, starting with January, therefore August has 6 letters.
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