28.08.2012, 20:39
The number can't exist for one simple reason:
No matter what order you place the numbers, one number will always result in not being the exact double of the one before simply because when they switch places, their value never changes.
Look at this example:
428
Now reversed, the first digit matches, it becomes an 8 which is a double of a 4. The second digit becomes a 2, which is equal to the digit before. The last part becomes a 4 which is half of the digit before. Let's not focus on the reasons for the outer digits but primarily the middle one. There is already one problem. On every unevent digit count, one digit never moves and thus can never be exchanged by a digit that could be times two the size.
Another problem is this:
48
Reversed, the first digit would equal 8, which is double of 4 but there is a big catch to this. Because you previously know that if your first digit is four, your second digit must be 8. However in reverse, 8 will be replaced by 4 which is half of the original digit.
There are a sum more problems that can occure and for these simple reasons, I do not believe there can be a number that reversed is equal the size times two.
No matter what order you place the numbers, one number will always result in not being the exact double of the one before simply because when they switch places, their value never changes.
Look at this example:
428
Now reversed, the first digit matches, it becomes an 8 which is a double of a 4. The second digit becomes a 2, which is equal to the digit before. The last part becomes a 4 which is half of the digit before. Let's not focus on the reasons for the outer digits but primarily the middle one. There is already one problem. On every unevent digit count, one digit never moves and thus can never be exchanged by a digit that could be times two the size.
Another problem is this:
48
Reversed, the first digit would equal 8, which is double of 4 but there is a big catch to this. Because you previously know that if your first digit is four, your second digit must be 8. However in reverse, 8 will be replaced by 4 which is half of the original digit.
There are a sum more problems that can occure and for these simple reasons, I do not believe there can be a number that reversed is equal the size times two.