math
posted by steven g. rosario on .
i am a three digit number. my hundreds digit is three more than my ones digit.my tens digit is oneless than my hundreds digit. what numbers can i be?

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