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Proving a Conjecture

After reading Calvin's comment regarding my solution for my Problem - Coins & Lines I tried to prove this statement mathematically but failed. Can someone please post a "Mathematical Proof" to this problem.

Restating the conjecture : There are only two "different" ways to place 10 identical coins in such a way that they lie in 5 straight lines & on each line there are exactly 4 coins.

NOTE : Here "different" means do not consider an arrangement that is rotated slightly as a completely different way.

Also please help me re-stating this problem in better way if possible.

Note by Gaurish Korpal
2 years, 9 months ago

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