Today’s ‘Wordle’ #1407 Hints, Clues And Answer For Saturday, April 26th

To solve this problem, we need to determine the number of ways to set the non-inducible elements in a list to inducible elements such that all elements in the list become non-inducible.

Let’s break down the approach:

1. Generate Toggle States: We need to generate all possible toggle states for the list elements. Each element can either be inducible or non-inducible. We will represent each toggle state using a binary number where 0 indicates non-inducible and 1 indicates inducible.

2. Toggle Each State: For each toggle state, we will simulate the effect of setting non-inducible elements to inducible. This will result in a toggled list where each element is either inducible or non-inducible based on the toggle state.

3. Check Uniformity: After toggling each state, we will check if all elements in the resulting list are the same. This will be true only if all non-inductive elements were toggled to inducible.

4. Count Valid States: We will count how many toggle states result in a uniformly non-inductive list.

Solution Code

def calculate_inducible(list_items):
    n = len(list_items)
    count = 0
    for i in range(2 ** n):
        toggled_list = []
        for x in list_items:
            if i:
                toggled_list.append('inducible')
            else:
                toggled_list.append('non-inducible')
        # Check if all elements in toggled_list are the same
        unique = set(['inducible', 'non-inducible'] if i else ['non-inducible', 'inducible'])
        if len(unique) == 2:
            count += 1
    return count

Explanation

1. Generated Toggling States: For each possible value of i (which ranges from 0 to 2^N – 1), we generate a toggle state. For each element in the input list, we toggle its state to either inducible or non-inducible based on the value of i.

2. Simulated List Check: We then simulate the effect of each toggle state to create a new list where non-inductive elements are toggled to inducible.

3. Uniformity Check: We check if the resulting list has all elements the same. This is true only if all non-inditive elements were toggled to inducible elements.

4. Count Valid States: We count how many toggle states result in a uniformly non-inductive list and return this count.

This approach ensures that we efficiently check each possible toggle state and count the number of valid states where all non-inductive elements are toggled to inducible elements to achieve a uniformly non-inductive list.