The second quotation below keeps mentioning "bijection", but it never explicitly defines it. So what's the formula for that bijection?
[A story instead of stars and bars - Making Your Own Sense](https://blogs.adelaide.edu.au/maths-learning/2015/10/17/a-story-of-stars-and-bars/)
> On to the third problem. As I said earlier, many people teach students to reduce other problems to this, and then remember a formula for the number of ways to solve this. I, on the other hand, still tell the same sort of story. This time, I imagine starting with the equation 0 + 0 + 0 = 0, and then moving along the positions. At each stage I can add 1 to the number there currently, or I can move ahead to the next position. As long as I add 1 ten times, it will work. Once more, I can represent this with a picture. I’ve got “+1” for the action of increasing a position by 1, and and arrow for moving to the next position. The picture shows how to get 3+2+5=10 and 6+0+4=10. Except for the change of symbols, the pictures are the same as the other ones, so the number of solutions is still 12C2.
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> [](http://blogs.adelaide.edu.au/maths-learning/files/2015/10/balloon-problem-03.png)
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> Sweet!
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> In the traditional stars and bars method, the stars represent objects and the bars represent dividers between them. In my method, the symbols always represent instructions in a story of how the collection/allocation/solution is constructed. And yes the symbols do always match the context of the problem. I find this much easier to remember and apply. Plus it’s cuter!
[Integer Equations - Stars and Bars | Brilliant Math & Science Wiki](https://brilliant.org/wiki/integer-equations-star-and-bars/)
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DNB
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2021-07-09T05:52:06Z (over 3 years ago)