SOLUTION: Find a six-digit number containing no zeros and no repeted digits in which the first digit is four more than the sixth digit, and the fourth and fith digit when read as a single nu

Question 534001: Find a six-digit number containing no zeros and no repeted digits in which the first digit is four more than the sixth digit, and the fourth and fith digit when read as a single number equal the product of the first and sixths digits.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a six-digit number containing no zeros and no repeated digits
a,b,c,d,e,f
:
I don't think there is enough information here to get a single solution.
We need some clue for b and c
:
in which the first digit is four more than the sixth digit,
a = f+4
Then a possible values: 5, 6, 7, 8, 9
then f:
has corresponding values 1, 2, 3, 4, 5
:
the fourth and fifth digits, when read as a single number, equal the product of the first and sixth digits.
10d + e = a*f
replace a with (f+4)
10d + e = f(f+4)
10d + e = f^2 + 4f
then try
f=5: 25+20 = 45, excluded because of repeated digit,5.
;
f=4: 16+16 = 32, this may work
8_ _ 3 2 4, choose the other digit from 1,5,6,7,9
:
f=3: 9+12 = 21, try this one
7 _ _ 2 1 3, choose the other digits from 4,5,6,8,9
:
f=2: 4+8 = 12, excluded because of repeated digit, 2
:
f=1: 1+5 = 5, excluded because we need two digits, no zero allowed
:
I think that is about all we can do with it

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