SOLUTION: I am a four-digit number. My thousands digit is 5 more than my hundreds digit, and my ones digit is the sum of my thousands and hundreds digits. My tens digit is the difference of

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Question 623888: I am a four-digit number. My thousands digit is 5 more than my hundreds digit, and my ones digit is the sum of my thousands and hundreds digits. My tens digit is the difference of my thousands and hundreds digits. What number am I?
Answer by solver91311(24713) (Show Source):
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Let represent the 1000s digit, represent the 100s digit, represent the 10s digit, and represent the 1s digit.

Constraints, each digit in the range

From the first given relationship:

So we know that otherwise

From the second relationship: , but by substitution we can write . This further restricts so that

From the third relationship:

So the number is 7259 or 6157 or 5055

John

My calculator said it, I believe it, that settles it