Sheikh `Abd al-Rahmân al-`Ajlân, lecturer at the Grand Mosque in Mecca
A person who is unsure of the number of Ramadan fasts missed is obligated to fast whatever number it takes to be certain that he or she has made up all the missed fasts. He or she can overestimate if need be.
However, the person should also take care not exaggerate the estimate or allow unfounded doubts to cause him or her to increase the number of days unreasonably.
And Allah knows best.
Source: Islam Today