Do you need 31 different LEDs, each controlled by 31 different buttons?
Are the 31 LEDs located in the same place, or scattered about? Are the 31 buttons located in the same place, or scattered about?
If each transmitter and receiver is independent, then you will need 31 of each of them. You will also need 62 batteries.
But if the 31 buttons are in the same place, and the 31 LEDs are together, then it can be done with one transmitter and one
receiver. You just need to give each button/LED pair a unique digital ID.