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I've looked everywhere for a solution, but the problem is I'm not a mathematician so have no frame of reference.

I'm trying to split a number up by ratio. For example, if you take the number 10:

  • If the smallest partition is 3, the result is 3, 7
  • If the smallest partition is 2, the result is 2, 3, 5
  • If the smallest partition is 1, the result is 1, 2, 3, 4

Any help would be much appreciated.

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    So let's say I have 100 ranks in a system and a total of 1,000,000 XP. I want to create a series of ranks that are increasingly harder to obtain and gaining 1,000,000 XP means you're at the highest rank. Also the lowest rank threshold can be set to a number, e.g., 500. Does that make things clearer?2012-05-29

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From the comments, you want 100 numbers satisfying $500=m_1\lt m_2\lt\cdots\lt m_{100}$ and $m_1+m_2+\cdots+m_{100}=1000000$ and you want the numbers $m_{i+1}-m_i$ to be roughly equal. If they were exactly equal, say, $m_{i+1}-m_i=d$ for all $i$, you'd have a 100 term arithmetic progression, starting with 500, and summing to 1000000. You'd have $m_{100}=500+99d$, and you'd have $50(1000+99d)=1000000$ That's $1000+99d=20000$, $99d=19000$, $191\lt d\lt192$ if I've done my arithmetic right. So you could make some of the steps 191, and the rest of them 192.

Now, you might want round numbers. In that case, you could make some of the steps 150, some of them 200 or 250. You've got a fair bit of room to play around with the numbers. Try out some schemes, and see what looks nice to you.

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    OK, I've been lea$r$ning. Understand now.2012-05-29