Question: Ali-Baba is a prisoner of the $42$ thieves who have just stolen $41$ identical magic incense sticks. The thieves want share this loot in such a way that everyone has exactly the same pieces as the others. Ali-Baba offers his know-how in exchange for his freedom. Ali arranges the $41$ sticks side by side, moves some pieces, then, after a few cuts carried out using a sword, between which he moves the pieces again, he gives each of the $42$ thieves exactly the same share made up of the same pieces.
Attribution: 16th international championship of mathematical games, day 1, question 16, available in the original French PDF.
What is the minimum number of cuts made by Ali-Baba? How many pieces will each of the thieves then have? Note: A cut can slice through a very large number of pieces of incense.
I literally have no idea how to approach this problem, tips and solutions would be appreciated.