Problem 414  Discussion Forum
Spoiler free discussion here!!
Remind me

Go to problem 
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 kdigit number like d_{1}d_{2}...d_{k} we can have a (k1)gon: [(d_{1},d_{2}), (d_{2},d_{3}), ..., (d_{k1},d_{k})] 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  5м:1w ago


lesnik7  5м:1w ago


sinan  5м:2w ago

edited*

C_K_Yang  5м:2w ago


sinan  5м:2w ago


nielkh  5м:2w ago

edited*

sinan  5м:3w ago


liuguangxi  5м:3w ago


1 
New Members
 nebula001 2d:21h
 PeterisP 1w
 Arun_CoDeR 1w
 hankim 2w:3d
 chfmoe 3w
Fresh Problems

Kimberling Sequence 1d:2h
solved by 6 
Palindromic Infinite Sequence 1w:1d
solved by 3 
Convergents of infinite sum 1w:5d
solved by 5 
Permutation Order II 2w:1d
solved by 8 
Integral circle packings 2 2w:4d
solved by 3