Elena Lucrezia Cornaro Piscopia, a 17th-century Venetian philosopher and mathematician, was the first woman to obtain a PhD. At this time, Italian society was passionate about debates on philosophy and mathematics, considered inseparable branches of knowledge. Mathematical logic problems are a clear example.

Use logic and numerical computation to solve the following problem.

A necklace broke

while two lovers played.

A row of pearls escaped:

the sixth part fell to the ground,

the fifth part remained in the bed,

the young woman saved the third part, 

her beloved picked up the tenth part,

and the cord remained with six pearls.

Tell me, reader, how many pearls did 

the necklace of the blessed have?