A city still does not have electric lighting, so candles are used in houses at night. In João's house, one candle is used per night, without burning it completely, and with four of these candle stubs, João makes a new candle. For how many nights can João light his house with 43 candles?
(a) 43
(b) 53
(c) 56
(d) 57
(e) 60
The correct option is (d).

With 43 candles, João's house can be lit for 43 nights, leaving 43 candle stubs. Since $43=4 \times 10+3$, with these 43 stubs, 3 stubs can be saved and 10 new candles can be made to light 10 nights. From these 10 candles, we get 10 stubs, which, together with the 3 that were left, give 13 stubs. Since $13=4 \times 3+1$, with these 13 stubs, 1 stub can be saved and 3 new candles can be made to light 3 nights. From these 3 candles, we get 3 stubs, which, together with the one that was left, give 4 stubs, with which we can make one more candle. Thus, in total, João's house can be lit for $43+10+3+1=57$ nights.