Wonderful and funny work. Bravi!
We have found a solution avoiding formulas, just eating loooooots of sweets!When Francesca takes two sweets, she takes one more than Olga (who has taken just one). When Francesca again takes four, she takes one more than Olga (who had taken three). So, in the end, Francesca has taken two more than her friend.In order to have 10 sweets more than Olga, Francesca needs to "help herself" ten times and so does Olga.Since no sweets are left, we can claim that in the box there were:1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=210 sweets!