Na svoj su medeni mjesec Tim i Lucy ponijeli sto kuverti s novcima koje su dobili na vjenčanju. Umjesto da ih složi jednu na drugu, Tim je u najveću kuvertu stavio preostalih
. Sve su kuverte različitih veličina i on ih je rasporedio tako da se za svake dvije različite kuverte ona manja nalazi unutar veće ili su jedna izvan druge. Pritom se i u manjoj i u većoj kuverti mogu nalaziti druge kuverte. Dva rasporeda smatramo različitima ako postoje dvije kuverte koje se u jednom rasporedu nalaze jedna unutar druge, a u drugom ne. Koliko ima različitih rasporeda kuverti?
Tim and Lucy took a hundred envelopes filled with money they received at their wedding on their honeymoon. Instead of stacking them one on top of the other, Tim placed the remaining
in the largest envelope. All the envelopes are of different sizes, and he arranged them so that for any two different envelopes, the smaller one is inside the larger one or they are separate from each other. Additionally, both the smaller and larger envelopes can contain other envelopes.
Two arrangements are considered different if there are two envelopes that are nested in one arrangement but not in the other. How many different arrangements of the envelopes are there?
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Na svoj su medeni mjesec Tim i Lucy ponijeli sto kuverti s novcima koje su dobili na vjenčanju. Umjesto da ih složi jednu na drugu, Tim je u najveću kuvertu stavio preostalih $99$. Sve su kuverte različitih veličina i on ih je rasporedio tako da se za svake dvije različite kuverte ona manja nalazi unutar veće ili su jedna izvan druge. Pritom se i u manjoj i u većoj kuverti mogu nalaziti druge kuverte.
Dva rasporeda smatramo različitima ako postoje dvije kuverte koje se u jednom rasporedu nalaze jedna unutar druge, a u drugom ne. Koliko ima različitih rasporeda kuverti?
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[lang=en]
Tim and Lucy took a hundred envelopes filled with money they received at their wedding on their honeymoon. Instead of stacking them one on top of the other, Tim placed the remaining $99$ in the largest envelope. All the envelopes are of different sizes, and he arranged them so that for any two different envelopes, the smaller one is inside the larger one or they are separate from each other. Additionally, both the smaller and larger envelopes can contain other envelopes.
Two arrangements are considered different if there are two envelopes that are nested in one arrangement but not in the other. How many different arrangements of the envelopes are there?
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