Marinada '26

[lang=hr] Val ima $99$ praznih vreća i za svaki cijeli broj $n$ neograničenu količinu kuglica mase $3^n$. Val je rasporedio u vreće konačno mnogo kuglica tako da nijedna vreća ne bude prazna i da masa kuglica u svakoj vreći bude ista. Pritom nije iskoristio više od $k$ kuglica iste mase. Koja je najmanja moguća vrijednost $k$? Budući da Valu bitnije koliko ima do vrha, a ne na čemu je sad, kao rezultat upišite $100-k$ [/lang] [lang=en] The Wave has $99$ of empty bags and for each integer $n$ an unlimited amount of balls of mass $3^n$. Wave has arranged a finite amount of marbles in the bags so that none of the bags were empty and the mass of balls in each bag to be the same. He did not use more than $k$ balls of the same mass. Who is the smallest possible value of $k$? Since it is more important for Wave to reach the top, than worry where he is now, enter $100-k$ as the result [/lang]