What 4-digit number abcd satisfies this equation?
4 * abcd = dcba
Since so but if from the unit digit of we conclude that is odd but it is the multiple of which should be even . Therefore ,
Consider the unit digit after multiplying a number among by , we have already known it is
we have but is impossible because we conclude
Then consider the actual values of these number :
we have
When
When it is impossible , so is the unique solution .
The required number is
is an indeterminated equation , any number may be the solution of provided will be an integer :
because is an integer , must be a positive odd , but if is very large which makes to be greater than , we cannot construct a number with a digit ...
13b + 1 = 2c
c = (13b + 1)/2
because is an integer , must be a positive odd since for (b + 1) to be perfectly divisible by 2 it should be even. And if b+1 is even it follows that b is odd.
And therefore simplependulum started by trying all the odd integers which start from 1. And quite clearly, the next odd number is 3. Putting b as 3 results in c = 20. Since c lies between 0 and 9, b cannot be 3 or any integer greater than 3. Therefore, b = 1.
Hello, chinchu!
This is a classic puzzle.
It can be solved without Algebra, just common sense.
What 4-digit number satisfies: . ?
We have:
. .
In column-1, since is a digit ,
. . we see that
But if , column-4 says: . ends in 1 . . . impossible.
Hence: .
. .
In column-1, we see that: .
In column-4, ends in 2.
. . Hence: .
. .
We see that there is no "carry" from column-2.
. . Hence: .
. . Suppose
. . . .
. . In column-3, we have: . ends in 0 . . . impossible.
Hence: .
. .
In column-3, ends in 1.
. . Hence: .
Since
Solution:
. .