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For those struggling with test #7:
"Each polygonal type: triangle (P3,127=8128)(P3,127=8128), square (P4,91=8281)(P4,91=8281), and pentagonal (P5,44=2882)(P5,44=2882), is represented by a different number in the set."
This phrase basically means that the set that you've found cannot have duplicates in it.
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Project Euler #61: Cyclical figurate numbers
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For those struggling with test #7: "Each polygonal type: triangle (P3,127=8128)(P3,127=8128), square (P4,91=8281)(P4,91=8281), and pentagonal (P5,44=2882)(P5,44=2882), is represented by a different number in the set."
This phrase basically means that the set that you've found cannot have duplicates in it.