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Q: What is the smallest six-digit number whose digits are all odd?

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22

111111 Any 6 digit number less than that would require a 0, which is an even number.

Find a four digit number whose digits will be reversed when multiplied by nine?

11

1414 is apparently both a triangular number and the smallest triangular number with four digits. It is also the Decimal expansion of sqrt(2) truncated and rounded to 4 places. There are many other mathematically esoteric aspects of 1414 if you care to check them out. 1414 is the smallest number whose square contains 3 consecutive 9's.1414 is the smallest number whose square contains 3 consecutive 9's. from http://www.celsius1414.com/mathematics

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17

111111

The smallest prime number, of course, is 2. The smallest prime number whose digits add up to 2 is, of course, 2. The next-smallest is 11. It is left as an exercise for the reader to determine whether the other numbers whose digits add up to 2 (e.g. 101, 1001, 10001) are prime.

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I think it will be 17. The sum of digits is 8, which is the cube of 2.

-11

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774774774774

none

Smallest is 11 & Largest is 77.

111111 Any 6 digit number less than that would require a 0, which is an even number.

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