# N heart

We define $$n\heartsuit$$ recursively as follows. $1\heartsuit =1;\ n\heartsuit = ((n-1)\heartsuit)\cdot n +1$ Find the largest $$n<1000$$ such that the last two digits of $$n\heartsuit$$ are zeroes.

Details and assumptions

Just to make it clear: unlike "n-factorial," "n-heart" is NOT an official mathematical terminology.

Clarification: There is no restriction / requirements on the third last digit.

Clarification: We can calculate that $$2 \heartsuit = (1\heartsuit) \cdot 2 + 1 = 1 \cdot 2 + 1 = 3$$ and $$3 \heartsuit = ( 2 \heartsuit) \cdot 3 + 1 = 3 \cdot 3 + 1 = 10$$.

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