Thread: Reverse digits problem

What five digit number when multiplied by 4 produces a five digit number whose digits are those of the original number but in reverse order?

Originally Posted by Ian Moore

What five digit number when multiplied by 4 produces a five digit number whose digits are those of the original number but in reverse order?

The leading digit can only be 1 or 2, and as when multiplied by 4 you get the
digits reversed it cannout be 1 (as then we would have an even number ending in 1),
so the number is of the form 2 . . . 8

Now the next most significant digit must be 0, 1 or 2 (as there is no carry when
multiplied by 4), and trial and error show that 21978 * 4 = 87912

RonL

Hello, Ian!

Here is a start on the problem . . .

What five-digit number, when multiplied by 4, produces a five digit-number
whose digits are those of the original number but in reverse order?

The problem looks like this:

. . .


In column-1: . . . . Hence: .

In column-5: . is even . . . Hence: .

. . .


In column-1: .
In column-1: . . . . Hence: .

. . .


In column-2: . ... and there is no "carry" to column-1.
. . Hence: .


Can you finish it?

Thankyou Soroban and Captain Black.
Much appreciated.