26. 2.13 Xuan Tai placed 365 cards on the incense, with different numbers written on their backs. Vasya can pay one ruble to choose any three cards and ask Betya to arrange them from left to right in the order of the numbers written on their backs. Can Vasya achieve the following goal by paying 2000 rubles: to arrange all 365 cards from left to right in the order of the numbers written on their backs on the table?
Parse Vasya may achieve the goal. To prove this, we first give a lemma.

Lemma: Suppose Vasya pays $x$ rubles to arrange $N-1$ cards in the required order on the table, where $N \leqslant 3^{k}$. Then he needs to pay no more than $k$ rubles to place the remaining one card in the correct position, that is, he needs to pay no more than $x+k$ rubles in total.

We will prove this lemma by induction. The case $k=1$ is obvious. Assume the lemma holds for all $N \leqslant 3^{k-1}$, we will prove it for $N \leqslant 3^{k}$. Clearly, Vasya's first step should be to determine the position of the $N$-th card relative to the cards $A$ and $B$ placed at the $\left[\frac{N}{3}\right]$-th and $\left[\frac{2 N}{3}\right]$-th positions. Since cards $A$ and $B$ divide the already arranged cards into three segments, Vasya uses 1 ruble to determine which segment the $N$-th card is in. Since each segment contains no more than $3^{k-1}-1$ cards, according to the induction hypothesis, Vasya needs to pay no more than $k-1$ rubles to further determine the position of the $N$-th card among them. The lemma is proved.

Next, we use the lemma to prove that Vasya can achieve his goal by spending no more than 2000 rubles. To arrange the first three cards, he spends 1 ruble. To insert the 4th to 9th cards (a total of 6 cards), Vasya spends no more than 2 rubles on each card. To insert the 10th to 27th cards, he spends no more than 3 rubles on each card. To insert the 28th to 81st cards, he spends no more than 4 rubles on each card. Next, he spends no more than 5 rubles on each of the 82nd to 243rd cards, and no more than 6 rubles on each of the 244th to 365th cards. This means Vasya needs to spend
$$
1 + 6 \times 2 + 18 \times 3 + 54 \times 1 + 162 \times 5 + 122 \times 6 = 1845 < 2000 \text{ (rubles) },
$$
to achieve his goal.