Posted by steven g. rosario on Thursday, August 16, 2012 at 5:30am.
d = your digit
d = 100 x + 10 y + z
my hundreds digit is three more than my ones
x = z + 3
that is equivalent with :
z = x - 3
my tens digit is oneless than my hundreds
y = x - 1
d = 100 x + 10 y + z
d = 100 * x + 10 * ( x - 1 ) + x - 3
d = 100 x + 10 x - 10 + x - 3 = 111 x - 13
Solution 1 :
x = 9
y = x - 1 = 9 - 1 = 8
z = x - 3 = 9 - 3 = 6
d = 986
Solution 2 :
x = 8
y = x - 1 = 8 - 1 = 7
z = x - 3 = 8 - 3 = 5
d = 875
Solution 3 :
x = 7
y = x - 1 = 7 - 1 = 6
z = x - 3 = 7 - 3 = 4
d = 764
Solution 4 :
x = 6
y = x - 1 = 6 - 1 = 5
z = x - 3 = 6 - 3 = 3
d = 653
Solution 5 :
x = 5
y = x - 1 = 5 - 1 = 4
z = x - 3 = 5 - 3 = 2
d = 542
Solution 6 :
x = 4
y = x - 1 = 4 - 1 = 3
z = x - 3 = 4 - 3 = 1
d = 431
Solution 7 :
x = 3
y = x - 1 = 3 - 1 = 2
z = x - 3 = 3 - 3 = 0
d = 320
Just start by putting 0, 1,2, ... into the ones digit
then fulfilling the other two conditions
320
431
542
653
764
875
986 , can't use 7 or higher for the unit digits