An interesting numbers problem this week.
You have a five-digit number. From this you produce two six-digit numbers A and B by placing a one before the number and after the number respectively.
The number B is three times bigger than the number A.
So what is the original five-digit number?
Let N be the original number.
A = 100,000 + N
B = 10N + 1
and because 3A = B
3(100,000 + N) = 10N + 1
300,000 + 3N = 10N + 1
299,999 = 7N
42,857 = N
To verify this, A = 142,857 and B = 428,571 and
3 x 142,857 = 428,571