Question 127
The number $1089$ has an interesting property. When we multiply this number by $9$, as shown below,
| 1 | 0 | 8 | 9 |
| :--- | :--- | :--- | :--- |
| | | $\times$ | 9 |
| 9 | 8 | 0 | 1 |
we get the number $9801$ which is the number $1089$ with their Numbers written from left to right!
a) Find a number of five digits $A B C D E$ such that its multiplication by $9$ is equal to the number that has the digits of $A B C D E$ written from the right To the left, that is,
| $A$ | $B$ | $C$ | $D$ | $E$ |
| :---: | :---: | :---: | :---: | :---: |
| | | | $\times$ | 9 |
| $E$ | $D$ | $C$ | $B$ | $A$ |
b) Find all seven digit numbers whose multiplication by $9$, as before, inverts the position of their digits.
| 1 | 0 | 8 | 9 |
| :--- | :--- | :--- | :--- |
| | | $\times$ | 9 |
| 9 | 8 | 0 | 1 |
we get the number $9801$ which is the number $1089$ with their Numbers written from left to right!
a) Find a number of five digits $A B C D E$ such that its multiplication by $9$ is equal to the number that has the digits of $A B C D E$ written from the right To the left, that is,
| $A$ | $B$ | $C$ | $D$ | $E$ |
| :---: | :---: | :---: | :---: | :---: |
| | | | $\times$ | 9 |
| $E$ | $D$ | $C$ | $B$ | $A$ |
b) Find all seven digit numbers whose multiplication by $9$, as before, inverts the position of their digits.