Puzzle 325
What is the test to see...
...if a number is divisible by nine?
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Hint
What could we do with the digits?
Answer
If the sum of the digits is divisible by nine, so is the number.
Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.
For example, is 486451464 divisible by 9?
Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.
Is 42 divisible by 9? Not sure, you can then do:
4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.
Puzzle 326
What number comes next in this sequence:
1 2 6 24 120 {?}
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Answer
720.
Each term is a factorial, 6! = 1 x 2 x 3 x 4 x 5 x 6 = 720.
Puzzle 327
What number comes next in this sequence:
1 8 9 64 25 216 49 {?}
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Hint
Think of squares and cubes.
Answer
512.
Each term alternates between a square and a cube, 8 3 = 512.
Puzzle 328
What are the next two numbers in this sequence:
202 122 232 425 262 728 {?} {?}
Puzzle Copyright © Kevin Stone
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Answer
293 031: these are the numbers 20, 21, 22, 23 etc grouped into three digits.
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