25 lines
916 B
Python
25 lines
916 B
Python
#!/usr/bin/env python
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from collections import Counter
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def decompose_sum(s):
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return [(a,s-a) for a in range(2,int(s/2+1))]
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# Generate all possible pairs
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all_pairs = set((a,b) for a in range(2,100) for b in range(a+1,100) if a+b<100)
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# Fact 1 --> Select pairs for which all sum decompositions have non-unique product
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product_counts = Counter(c*d for c,d in all_pairs)
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unique_products = set((a,b) for a,b in all_pairs if product_counts[a*b]==1)
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s_pairs = [(a,b) for a,b in all_pairs if
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all((x,y) not in unique_products for (x,y) in decompose_sum(a+b))]
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# Fact 2 --> Select pairs for which the product is unique
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product_counts = Counter(c*d for c,d in s_pairs)
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p_pairs = [(a,b) for a,b in s_pairs if product_counts[a*b]==1]
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# Fact 3 --> Select pairs for which the sum is unique
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sum_counts = Counter(c+d for c,d in p_pairs)
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final_pairs = [(a,b) for a,b in p_pairs if sum_counts[a+b]==1]
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print(final_pairs)
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