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?

solution:

Let the number be ABCDE

>>The second digit is three times the fourth digit<<

So D is 1,2, or 3 and B is 3,6 or 9.

The number is A3C1E, A6C2E, or A9C3E

>>The second digit is ... five more than the fifth digit.<<

That rules out 3 for B, so B is 6 or 9, and D is 2 or 3.

It also tells us that E is 1 or 4, so that B can be 5 more than it.

So the number is A6C21 or A9C34

>>The third digit is ... twice the fourth digit<<

So C is twice D, which is 2 or 3. So C is 4 or 6

So the number is A6421 or A9634

>>The third digit is one-half the first digit

So C is 4 because 6 is too large to be half a digit. And so

A has to be 8 so that C=4 can be half of it.

So the number is 86421.