Question 344587: A number has five digits, none of which are zero. The first digit plus the second digit equals the third digit. The third digit times two, plus the second digit, equals the fifth digit. The second digit times two equals the first digit. The first digit times four equals the fourth digit. The fourth digit minus the second digit equals the fifth digit. What is the number?
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website! Let the 1st, 2nd, 3rd, 4th, and 5th digits be F, S, T, H, and I, respectively
Then S = S
T = F + S
I = 2(F + S) + S___I = 2F + 2S + S___I = 2F + 3S
F = 2S
H = 4F
Now, since 1st digit or F = 2S, we can say that:
T = F + S_____T = 2S + S, or 3S
H = 4F____H = 4(2S)____H = 8S
I = 2F + 3S____I = 2(2S) + 3S___I = 4S + 3S____I = 7S
Now we can see that:
F = 2S
S = S
T = 3S
H = 8S
I = 7S
We can also see that the largest digit is the 4th digit as H = 8S
Now, it’s clear that S or the 2nd digit CANNOT be any digit from 2 – 9 as this would yield a 2-digit number (e.g. 8 * 2 = 16)
This means that S or the 2nd digit has to be less than 2, and since it’s given that it CANNOT be 0, then S must equal 1
Therefore:
F = 2S = 2(1) = 2
S = S = 1
T = 3S = 3(1) = 3
H = 8S = 8(1) = 8
I = 7S = 7(1) = 7
This makes the 5-digit number: 
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