At Brilli's zoo, she is trying to train a monkey to learn how to count. The monkey is given a stack of cards, numbered 1 to 30, in some random order. The cards are laid out from left to right. Each time the monkey moves the card numbered i+1 to the immediate right of the card numbered i, he gets a banana. Otherwise, the monkey gets an ant bite and has to undo his move. What is the most number of bananas that the monkey can get?

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29 To determine the most number of bananas the monkey can get, we need to find the longest increasing subsequence in the given stack of cards.

There are different approaches to solve this problem, but one of the efficient ways is using dynamic programming.

Let's define an array `dp` of size 30, where `dp[i]` represents the length of the longest increasing subsequence that ends at card `i`.

Initially, all elements of `dp` are set to 1 since each card can form a subsequence of length 1 itself.

Now, for each card `i` from 1 to 30, we iterate over all the previous cards `j` from 0 to i-1. If the value of the card `j` is less than the value of card `i`, we can potentially extend the longest increasing subsequence ending at card `j` by placing card `i` to the right of it. In that case, we update `dp[i]` as `max(dp[i], dp[j] + 1)`.

After iterating over all the cards, we find the maximum value in the `dp` array, which represents the length of the longest increasing subsequence.

The most number of bananas the monkey can get will be this maximum value since each move to the right will represent one banana.

Let's break down the steps to find the most number of bananas:

1. Create an array `dp` of size 30 and initialize all elements to 1.
2. For each card `i` from 1 to 30:
- Iterate over all previous cards `j` from 0 to i-1.
- If card `j` is less than card `i`, update `dp[i]` as `max(dp[i], dp[j] + 1)`.
3. Find the maximum value in the `dp` array.
4. This maximum value represents the length of the longest increasing subsequence, which is the most number of bananas the monkey can get.

Implementing these steps will give you the desired result.