# More Dice

Discrete Mathematics Level pending

We have $$n^2$$ dice labelled from $$d_{1}$$ to $$d_{n^2}$$, where every dice has the numbers $$1,2,3,...,n^2$$ on its faces. We roll all the dice simultaneously, and denote $$f(d_{i})$$ as the number which comes up on $$d_{i}$$. It is given that $$d_{i} \ne d_{j}$$ for all $$i \ne j$$. Define: $g(n) = \displaystyle\sum_{k=1}^{\lfloor \dfrac{n^2}{2} \rfloor} f(d_{k})$ Given that $$n$$ is the smallest positive integer such that it is possible that $\displaystyle\sum_{k=1}^{\lfloor \dfrac{n^2}{2} \rfloor} f(d_{k}) : \displaystyle\sum_{k=\lfloor \dfrac{n^2}{2} \rfloor+1}^{n^2}f(d_{k}) = 2 : 5$ What is $$g(n)$$?

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