Question

IFABCD = (ABC) x (BD), where A, B, C and D are digit not necessarily distinct, then the value of C is:

Answer 1

Answer:

let, a=2n

1

+1,b=2n

2

+1,c=2n

3

+1,d=2n

4

+1 where n

i

∈N

⟹2n

1

+1+2n

2

+1+2n

3

+1+2n

4

+1=20

⟹2n

1

+2n

2

+2n

3

+2n

4

=16

⟹n

1

+n

2

+n

3

+n

4

=8

Number of solutions or ordered pairs for this equation are given by

n+r−1

C

r−1

=

8+4−1

C

4−1

=

11

C

3

=165