ABCD is a 4 digit number find out ABC with the following hints ?

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ABCD is a 4 digit number find out ABC with the following hints
A is not equal to B and C
B is not equal to C
A<B<C
D is not equal to 0(zero) and 1(one)
If A+B+C+D = XY(two digit number)
Then X+Y=D-1

posted Oct 6, 2015

Lets work backward -
What we know XY is two digit and X+Y+1=D which is one digit i.e. 9 or less.

Lets assume D is 9 then X+Y=8 such means X*Y can be (6,2)12, (5,3)15, (4,4)16
1) Now if X*Y is 12 (we know D is 9)
=>A+B+C=3 not possible

2) Now if X*Y is 15 (we know D is 9)
=>A+B+C= 6 i.e. A=1, B=2, C=3 (a solution)

3) Now if X*Y is 16 (we know D is 9)
=>A+B+C=7 i.e. A=1, B=2, C=4 (a solution)

Possible Solutions are
1) A=1, B=2, C=3, D=9
2) A=1, B=2, C=4, D=9

A = 1;
B = 3;
C = 4;
D= 2;
A + B + C + D = 10
X = 1, Y = 0
X + Y = 1 + 0
= 1
= 2 -1
= D-1

X*Y=10 then X can not be 1 with Y as zero, please cross check your solution.

There can be as many solutions as possible but my own is ABCD = 1254

answer Oct 7, 2015 by anonymous
In this case it came as A+B+C+D = 12 which means x,y are 12,1 or 6,2 or 4,3 which puts D as X+Y-1 i.e. 9 or 8 so answer seems to be wrong

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