Question 42
A four digit number not ending with $0$ is written on the blackboard.
Carlos has multiplied the number on the blackboard by $4$, added $30$ to the result and written the obtained number in his notebook.
Dora has written in her notebook the number which is obtained when reading the digits of the number on the blackboard in reverse order. (For instance, if the number on the blackboard is $3702$, Dora writes the number $2073$ in her notebook.)
It turns out that Carlos and Dora have written the same number in their notebooks.
Find all possible values of the number on the blackboard.
Carlos has multiplied the number on the blackboard by $4$, added $30$ to the result and written the obtained number in his notebook.
Dora has written in her notebook the number which is obtained when reading the digits of the number on the blackboard in reverse order. (For instance, if the number on the blackboard is $3702$, Dora writes the number $2073$ in her notebook.)
It turns out that Carlos and Dora have written the same number in their notebooks.
Find all possible values of the number on the blackboard.