Nisu svi bili zadovoljni ovim načinom podjele ljubičica. Prvi se pobunio Vladek: "Kakva je ovo nepravda!? Jesam li se ja za ovo borio??". "Nisi se ni za što borio, piskaralo kukavičko", uzvratio mu je bijesno Al. "Smirimo se momci, sve se može riješiti mirnim razgovorom", pokušao je Teodor smiriti situaciju, ali prekasno. Al i Vladeka glasno su se prepirali, a ni ostali nisu željeli propustiti akciju pa su se priključili jedni Alu, drugi Vladeku. Josip zvani Broz pokušao je ostati nesvrstan i daleko od nastale gungule, no nije mogao dopustiti takvo divljaštvo u Rajskoj jami: "Dosta, dosta je bilo! Van svi! Da te ne vidim Vladek! Napolje! Marš Ale!" "Ti to meni tako, ha?", dovikne mu Al, "Ma ionako nisam htio biti u ovaj rupi."
I tako je kraju došao njihov posjet Rajskoj jami, ali ne i problemima. Sva su desetorica u grupi stajala pred vratima, ali prije nego što smiju izaći moraju se podijeliti na sljedeći način: u prvom koraku dio grupe se odvaja u zasebnu grupu tako da sada budu dvije neprazne grupe. U svakom sljedećem koraku od neke (jedne) postojeće grupe (koja se sastoji od barem dvije osobe) ponovno se odvaja manja grupa i to se ponavlja dok svatko od njih desetorice ne ostane stajati sam. Na koliko je načina moguće provesti ovaj postupak odvajanja?
Not everyone was happy with the way the violets were distributed. Vladek was the first to complain: "What kind of injustice is this!? Is this what I fought for??" "You haven’t fought for anything, you cowardly scribbler," Al retorted angrily. "Let’s calm down, guys, everything can be resolved with a peaceful conversation," Teodor tried to diffuse the situation, but it was too late. Al and Vladek were arguing loudly, and the others didn’t want to miss out on the action, so they joined in—some on Al’s side, others on Vladek’s. Josip, known as Broz, tried to stay neutral and out of the chaos, but he couldn’t allow such rowdiness in Rajska jama: "Enough! That’s enough! Everyone out! I don’t want to see you again, Vladek! Get out! Out with you too, Al!" "You’re talking to me like that, huh?" Al shouted back, "I didn’t want to stay in this dump anyway."
And so, their visit to Rajska jama came to an end, but the problems didn’t. All ten of them stood together outside the door, but before they could leave, they had to divide themselves as follows: in the first step, part of the group splits off into a separate group so that there are now two non-empty groups. In each subsequent step, from one (existing) group that consists of at least two people, another smaller group splits off, and this continues until each of the ten ends up standing alone. In how many ways can this splitting process be carried out?
[lang=hr]
Nisu svi bili zadovoljni ovim načinom podjele ljubičica. Prvi se pobunio Vladek: "Kakva je ovo nepravda!? Jesam li se ja za ovo borio??". "Nisi se ni za što borio, piskaralo kukavičko", uzvratio mu je bijesno Al. "Smirimo se momci, sve se može riješiti mirnim razgovorom", pokušao je Teodor smiriti situaciju, ali prekasno. Al i Vladeka glasno su se prepirali, a ni ostali nisu željeli propustiti akciju pa su se priključili jedni Alu, drugi Vladeku. Josip zvani Broz pokušao je ostati nesvrstan i daleko od nastale gungule, no nije mogao dopustiti takvo divljaštvo u Rajskoj jami: "Dosta, dosta je bilo! Van svi! Da te ne vidim Vladek! Napolje! Marš Ale!" "Ti to meni tako, ha?", dovikne mu Al, "Ma ionako nisam htio biti u ovaj rupi."
I tako je kraju došao njihov posjet Rajskoj jami, ali ne i problemima. Sva su desetorica u grupi stajala pred vratima, ali prije nego što smiju izaći moraju se podijeliti na sljedeći način: u prvom koraku dio grupe se odvaja u zasebnu grupu tako da sada budu dvije neprazne grupe. U svakom sljedećem koraku od neke (jedne) postojeće grupe (koja se sastoji od barem dvije osobe) ponovno se odvaja manja grupa i to se ponavlja dok svatko od njih desetorice ne ostane stajati sam. Na koliko je načina moguće provesti ovaj postupak odvajanja?
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[lang=en]
Not everyone was happy with the way the violets were distributed. Vladek was the first to complain: "What kind of injustice is this!? Is this what I fought for??" "You haven’t fought for anything, you cowardly scribbler," Al retorted angrily. "Let’s calm down, guys, everything can be resolved with a peaceful conversation," Teodor tried to diffuse the situation, but it was too late. Al and Vladek were arguing loudly, and the others didn’t want to miss out on the action, so they joined in—some on Al’s side, others on Vladek’s. Josip, known as Broz, tried to stay neutral and out of the chaos, but he couldn’t allow such rowdiness in Rajska jama: "Enough! That’s enough! Everyone out! I don’t want to see you again, Vladek! Get out! Out with you too, Al!" "You’re talking to me like that, huh?" Al shouted back, "I didn’t want to stay in this dump anyway."
And so, their visit to Rajska jama came to an end, but the problems didn’t. All ten of them stood together outside the door, but before they could leave, they had to divide themselves as follows: in the first step, part of the group splits off into a separate group so that there are now two non-empty groups. In each subsequent step, from one (existing) group that consists of at least two people, another smaller group splits off, and this continues until each of the ten ends up standing alone. In how many ways can this splitting process be carried out?
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