33 lines
1.3 KiB
Python
33 lines
1.3 KiB
Python
from itertools import combinations
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# Step 1: Define the set and target sum
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numbers = list(range(1, 9))
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target = 9
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# Step 2: Generate all 5-number combinations
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valid_combinations = list(combinations(numbers, 5))
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# Step 3: Define the 4 mutually exclusive pairs that sum to 9
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pairs = [(1, 8), (2, 7), (3, 6), (4, 5)]
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# Step 4: Check each combination for the required condition
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def has_pair_summing_to_target(combo, pair_list):
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for a, b in pair_list:
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if a in combo and b in combo:
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return True
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return False
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# Step 5: Verify each combination
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always_has_pair = all(has_pair_summing_to_target(c, pairs) for c in valid_combinations)
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print(f"Every 5-number combination has at least one pair summing to {target}: {always_has_pair}")
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'''
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The code verifies if every 5-number combination from 1 to 8 contains at least one of the specified pairs that sum to 9.
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# Output: True or False based on the verification
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# Note: The output will be True since every combination of 5 numbers from 1 to 8 will always
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# include at least one of the pairs (1, 8), (2, 7), (3, 6), or (4, 5) due to the nature of combinations and the range of numbers.
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How it works:
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1. It generates all combinations of 5 numbers from the set {1, 2, 3, 4, 5, 6, 7, 8}.
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2. It checks each combination to see if it contains at least one of the pairs that sum to 9.
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''' |