-
raunakrajan
- Senior | Next Rank: 100 Posts
- Posts: 62
- Joined: Tue Mar 16, 2010 8:27 am
- Thanked: 1 times
Let me put them as a,b,c for our notation. So a,b,c are different,non-zero single digit numbers
now,
ab * ba =cbca
and
a(a+c) = b
a(a+c) = b
we know that b is a single digit
product of two single digits giving a single digit
how many cases:
1* (1+{2,3,4,5,6,7,8,9} )
Hence a=1 - Let us keep this for some time..
another possibility..
2*(2+1)
because c cannot be 2 if a=2. [different digits]
c cannot be 3 because b will become 10.
so a=2, c=1 -> let us keep this also aside
next:
3*(3+0)
this is not possible because c cannot be 0. And if c is greater than 0 them b is more than 10.
So for any value of "a" greater than 2, we will not have a feasible solution.
So now a has to be either 1 or 2.
when a=2, c=1, b= 6
coming to our other equation:
ab * ba =cbca
26*62=1612
This is satisfied.
Let us see what if a=1?
Look at the last digit of the product -> b*a is yielding last digit as "a"
if a=1, then last digit will be "b" and not "a"
Hence a cannot equal 1.
hence ab = 26
