Question 867342: Who am I?
I am a three digit number.
I am odd.
My ones digit is greater than my tens digit.
My hundreds digit is prime.
My tens digit is twice my hundreds digit.
Two of my digits are square numbers.
Found 2 solutions by richard1234, josmiceli:
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Suppose the 3-digit number is abc.
a is prime, and two digits are squares --> b, c are squares (in particular, c = 9 or c = 1).
If c = 1, then b = 0 (since c > b), but this implies a = 0, which doesn't work.
If c = 9, then b = 4 or 1. b cannot be 1 since b = 2a, so b = 4, and a = 2.
# = 249
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! It is odd, so the one's digit
is 1,3,5,7, or 9
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The tens digit is 2X the hundreds digit,
so, the tens digit is even
The ones digit is greater than the tens digit,
so the tens digit is either 2,4,6, or 8
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The hundreds digit is prime, so it is
either 1,3,5,7, or 9
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The tens digit is 2X the hundreds digit, so
the tens digit is either 2 or 6
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Two of the digits are square numbers. Since the
tens digit is either 2 or 6, then both the
units digit and the hundreds digit are
square numbers
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The hundreds digit must be 1, since 1 is the square
of 1 and then the tens digit can be 2 ( twice the
hundreds digit )
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The ones digit is greater than the tens digit,
so it must be 9 ( which is square )
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The number is 129
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