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Question 391711: I am thinking of a five-digit number where the fifth digit is one-half the fourth digit and one-fourth the third digit. The third digit is one-half the first digit and twice the fourth digit. The second digit is three times the fourth digit and five more than the fifth digit. What is the five-digit number?
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Look for the most restrictive statement:
>>...the fifth digit is...one-fourth the third digit...<<
There are only two possibilities for that statement:
A. the fifth digit is 1 and the third digit is 4
or
B. the fifth digit is 2 and the third digit is 8
However
>>...The third digit is one-half the first digit...<<
Therefore 8 is ruled out as the third digit since 16 is not a digit.
So B is ruled out and we have
8_4_1
>>...The third digit is...twice the fourth digit.
So we have
8_421
>>...The second digit is three times the fourth digit...<<
So we have
86421
Note: We didn't need to know this piece of information:
>>...The second digit is...five more than the fifth digit...<<
Edwin
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
The 5th digit has to be either 1 or 2. If the 5th digit were zero, then all of the digits would be zero which makes no sense. If the fifth digit were 3, then the 3rd digit would have to be 12 which is not a digit. So the 3rd digit is either 4 or 8. If the 3rd digit is 8, then the 1st digit would have to be 16 which is not a digit, so the 3rd digit must be 4. That means the 1st digit is 8, the 3rd digit is 4, the 4th digit is 2, and the 5th digit is 1. I'll leave it to you to figure out the 2nd digit.
John
My calculator said it, I believe it, that settles it
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