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I invented a new concept called Race of Work. It's based on Proof of Work, except there is no difficulty. Instead, there is a predefined time in each hour that consider being Block time. During the block time all the miners trying to find the smallest hash possible, and the one with the lowest hash wins. To simplify it lest call the hash search process by the method $F()$, it's output is the hash $H; 0 < H < 2^{32}$

I plan to use it in pools, but I am not sure about the rewards system. Here what I have in mind, please tell me if you think it will work or suggest a modification.

Whenever a miner finds a smaller number hash, he will send it to the pool. The pool will remember the smallest hash from each miner. In case the pool wins the block, here how it will reward the miners:

There are $N$ miners in the pool, each of the miner's hashes is a number, $H_i$ where $i$ is the miner id from $1$ to $N$.

The pool will pick some high number $K$ such that $K > max(H_i)$ and will calculate: $\frac{k}{H1} + \frac{k}{H2} + \frac{k}{H3}... + \frac{K}{H_i} = P$

Pools reward is R, it will give each miner $\frac{RK}{PH_i}$ coins.

Does my calculation make sense? What do you think about it?

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No, it doesn't. The factor $K$ is unnecessary; it drops out in the result. You're simply weighting the rewards with the reciprocals of the hashes. You could directly write

$$ R_i=\frac{H_i^{-1}}{\sum_iH_i^{-1}}\cdot R\;. $$

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