Problem 414 - Discussion Forum
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Take the number 134431001 as an example. We can make pairs using the 2 digits following one another:
[(1, 3), (3, 4), (4, 4), (4, 3), (3, 1), (1, 0), (0, 0), (0, 1)]

If we assume that these are the lattice points, we can draw line segments in the same order and we can have a polygon.



In general for a k-digit number like d1d2...dk we can have a (k-1)-gon:
[(d1,d2), (d2,d3), ..., (dk-1,dk)]


If the drawn polygon is a convex one then we will call this kind of number as convex number.

How many positive convex numbers are there?

Answer format: count,sum

[My timing: < 1m]

Notes:
- Any two neighbouring line segments cannot be collinear.
- All the generated pairs must be distinct.
- Some polygons can be generated by more than one number. 
  For example: 112321, 123211, 232112, 321123, 211232
  Since the numbers are different, they are all counted.



sinan - 2м:1w ago

lesnik7 - 2м:1w ago

sinan - 2м:2w ago
edited*

C_K_Yang - 2м:2w ago

sinan - 2м:2w ago

nielkh - 2м:2w ago
edited*

sinan - 2м:2w ago

liuguangxi - 2м:2w ago


1


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