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Question 1048393: I am a 6 digit number between 300,000 and 320,000. All of my digits are different. My hundreds digit is an odd number. My thousands digit is half the tens digit and is divisible by 10. The sum of the tens digit and the thousands digit is less than 10.
Attempt:
Steps for each sentence:
• I am representing the 6 digits using the variables: A B C D E, and F.
• The variables are decreasing left to right, thus A = 100,000 digit and F = 1s units.
• No repeating digits in A thru F
• D = is an odd digit between 1 and 9
• C = .5E, or 2C = E.
• C/10 = assuming a whole number must be 0
• B + D < 10
• A must be 3, because the number is between 300000 and 320000
Putting it all together:
A B C D E F
3 0 or 1 .5E 1,5,7,9 2C
A = 3
3 1 0 2 4 5
3 0 2 1 4 5
3 0 4 1 8 5
Possible Answers:
302, 145
304, 185
Answer by ikleyn(52810)   (Show Source):
You can put this solution on YOUR website! .
I am a 6 digit number between 300,000 and 320,000. All of my digits are different. My hundreds digit is an odd number. My thousands digit is half the tens digit and is divisible by 10. The sum of the tens digit and the thousands digit is less than 10.
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The condition is self-contradictory.
Find the contradiction inside. // It would be too much if I point you on the contradiction.
Don't litter the forum with wrong problems.
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Comment from student: What are you kidding? I try so solve a problem, and you are calling it a contradiction?
You are unwilling to point it out and then you further Denigrate the solution by stating don't litter the forum?
I'm asking for help not negative comments. What would be helpful is pointing out the contradiction and/or providing recommendations.
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My response. No, I am not kidding.
The condition says:
1. "All of my digits are different."
2. "My thousands digit is half the tens digit and is divisible by 10."
The only digit that is divisible by 10, is ZERO. Agree?
So, the thousand digit is zero.
In turn, it is half the tens digit, according to the condition. Hence, the tens digit is ZERO too.
Thus the thousands digit and the tens digit are both ZERO.
It contradicts to the statement "All of my digits are different."
This is why I called the condition self-contradicting.
No, I am not kidding.
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