Sroan 有一个私人的保险箱，密码是 7 个 不同的数字。 Guess #1: 9062437 G...

Solving the puzzle

The puzzle gives four 7-digit guesses, and the instruction is that each guess has exactly two correct digits in the correct spots, with no adjacent positions being correct. So, we know there are pairs of correct digits in each guess, but they aren't next to each other. To crack this, I'll focus on identifying the digits that repeat across various guesses in non-adjacent positions. It's a process of cross-referencing the guesses while respecting the non-adjacency condition. Let's figure it out step by step!

Breaking down the password puzzle

The puzzle states that for each guess, exactly two digits match in the correct spots, and these correct spots must not be adjacent. We're working with 4 guesses, each 7 digits long, with distinct digits. The goal is to identify the two correct non-adjacent positions for each guess. For example, guess 1 has guess digits positioned 1 to 7, and we need to find exactly two matching non-adjacent positions. It's a lot of logical deduction, but we can start systematically checking for matches in pairs and cross-referencing!

Analyzing password possibilities

We have an unknown password with distinct digits, and each guess provides exactly two correct digits in the correct spots (not adjacent). The strategy is to cross-check each guess and use the fact that every hit involves non-adjacent positions. Each guess's positions give us candidate digits, but only one guess's digit might match the password for that position. I'll start by examining each position from 1 to 7 to see which digits appear frequently across the guesses and eliminate possibilities accordingly. Let’s break down this process and see what fits!

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Solving with constraints

The task involves figuring out the correct digits for each column based on the guesses, along with the two-hit condition and the non-adjacency requirement. Essentially, we have a handful of valid possibilities for each column's digits, and we need to sum the total hits across all guesses. The tricky part here is ensuring we get exactly 8 hits and that the positions are non-adjacent. So, the strategy involves setting up hit counts for each column, and carefully assigning hits across guesses while respecting both the non-adjacency condition and the distinctness of digits in each column. Let's see how this comes together!

Assigning hits while avoiding adjacency

We have a lot of potential ways to assign hits to the columns, but we need to balance the digit possibilities while ensuring distinctness and meeting the conditions of adjacency. For each column, I’ll assign a guess, checking that the numbers are distinct and that the guesses' hit positions are not adjacent. Specifically, for guesses 3 and 4, the only extra hit can’t correspond to columns 4 or 6, since they’re adjacent to column 5. For guesses 1 and 2, positions can't be adjacent to each other. Lots of careful balancing to consider...!

Assigning columns and hits carefully

I need to assign columns to guesses and respect some constraints. For guesses 3 and 4, they get hits in column 5, but their extra hit can’t be in columns 4 or 6, since those share adjacency with column 5. For guesses 1 and 2, their hits can’t be adjacent. The trick lies in balancing these constraints while maintaining distinctness for all digits. Columns from {1, 2, 3, 7} are the key places for guesses 3 and 4. Time to check how to assign correctly, respecting all conditions!

Assigning positions for guesses

I’m working through assigning columns to guesses while respecting adjacency and non-adjacency constraints. For guesses 3 and 4, their extra columns can only be from {1, 2, 3, 7}, as columns 4 and 6 are off-limits due to their adjacency to column 5. Guess1 and guess2 have no restrictions except for non-adjacency between their assigned columns. I am systematically checking partitions of potential sets of positions, ensuring no adjacent pairs are assigned to the same guess. This involves some careful combinatorics!

Checking assignment possibilities

I'm assigning positions for different guesses, making sure to respect adjacency and frequency restrictions. For guesses 3 and 4, they must be assigned to columns that allow 3 and 4, which are {1, 2, 3, 7}. For guess1 and guess2, their columns must not be adjacent. I'm calculating the number of assignments by considering the various constraints, like the need for two 1’s and two 2’s in non-adjacent positions. There's some brute force required for determining all valid combinations, but the logic is coming together!

Exploring valid assignments for positions

I’m considering how to assign values to different positions, particularly guessing positions for 3 and 4 within the set {1, 2, 3, 7}. After assigning 3 and 4, I'm focusing on making sure that there are two 1's and two 2's in non-adjacent positions. I break down possible assignments, checking for constraints like adjacency and ensuring that each guess isn’t placed in consecutive cells. Some cases are ruled out, but I do find valid setups — like when x4 = 2, x6 = 1, and x7 = 2, which fits all conditions.

Identifying conflicts in Option A

I’m testing out various possible assignments for values, but I’m hitting conflicts where digits repeat. For instance, I had conflicts between a1 and a2, and a3 and a4. Even when trying other combinations, conflicts still arise due to overlapping digits. This makes option A unworkable. To move forward, I’ll need to test different placement scenarios for guesses for positions 1 and 3 — while making sure that the digits are distinct, and the non-adjacency rules are followed.

Checking valid assignments

I’m checking for valid assignments based on the constraints: each guess should have two distinct hits and non-adjacency between columns. For an option like (x2, x4, x6, x7) = (1, 2, 2, 1), there were conflicts that didn’t meet the distinct digits requirement. However, with (1,2,2,1), the digits are distinct, and the hits per guess satisfy all conditions. After calculating, I find 4053927 as a valid candidate password, meeting all the constraints for both column contents and non-adjacency rules.

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Evaluating assignments

Checking adjacency constraints: for example, positions x4, x6, and x7, where the only adjacency concern is between x6 and x7. Valid configurations for them are (1,1,2) and (1,2,1), but not (2,1,1). As we assign values to other positions like x1, x2, and x3, conflicts emerge, such as repeated digits like a2 and a4 both being 2. Trying other configurations like Option D and F also results in either conflicts or inability to assign values uniquely. Only certain assignments meet all constraints, leading to the same consistent solution.

Reasoned for 6m 15s

Mapping out strengths

I’m thinking about Taiyuan city's drone tourism, noting its advantages and short development period. This leads me to identify existing issues like inadequate risk control, safety protocols, limited public awareness, and underdeveloped business models and collaboration with other sectors.

Mimicking structure

I’m replicating the style and structure of the provided text for Taiyuan's drone tourism, highlighting advantages such as the city's rich historical context, geographical environment, and unique tourist attractions.

Reasoned for 4m 13s