Question 897071
Find a six-digit number 
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We put 6 blanks for the 6 digits:

_ _ _ _ _ _
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the second digit is eight more than the first, 
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Since the first digit can't be 0, then in order for there to be a
digit which is 8 more than the first, the first digit is 1 and
the second digit is 9.  So we have:

1 9 _ _ _ _
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(the second digit is) one more than the fourth, 
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So the fourth digit must be 8, so that 9 will be one more than it.

So we have:

1 9 _ 8 _ _
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and (the second digit is) two more than the last.
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So the last digit must be 7, so that 9 will be two more than it.

So we have:

1 9 _ 8 _ 7
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in which the first digit is one less than the third, 
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So the third digit is 2.  So we have

1 9 2 8 _ 7
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the third digit is one less than the fifth, 
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So the fifth digit is 3. So we have the entire number.

1 9 2 8 3 7
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and The sum of the first and fourth digits equals the second digit, 
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That's true, 1+8=9, but we didn't need to know that.
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the sum of the first and third digits equals the fifth, 
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That's true too, 1+2=3, but we didn't need to know that either.
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and the sum of all the digits is 30.
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That's also true, 1+9+2+8+3+7=30, but we didn't need to know that either.

Edwin</pre>