a+b+c+d = k
a

Question

a+b+c+d = k
a<b<c<d
everything is an integer
can you find the number of solutions as a function of K

dan815 · Answer

@TrojanPoem

trojanpoem · Answer

Solve this in front of me. And give me another example

dan815 · Answer

okay umm lemme show u why i think this relation is important one

dan815 · Answer

okay ill show u all my work so far, its not much lol

trojanpoem · Answer

:)

dan815 · Answer

okay so i started working backwards, now i allowed 0 to be in the first place of the digit, we can take care of the problems of that later on

dan815 · Answer

im looking at only the increasing case, and the decreasing case will be the same numbers

dan815 · Answer

so for 10 digit numbers we have 1 non bouncy number that is strictly increasing 
0123456789
and 1 non bouncy number that is strickly decreasing
9876543210

dan815 · Answer

if there were 2 strickly increasing then there have to be 2 strictly decreasing so you can see why we only care about one half

trojanpoem · Answer

123  increasing
321 decreasing
456 inc
654 dec ( non bouncy) all )

dan815 · Answer

yes that is correct

dan815 · Answer

okay now lets move to the 9 digit case

dan815 · Answer

here is where we can see the pattern

trojanpoem · Answer

123456789
987654321

dan815 · Answer

leets only look at the increasing for now

trojanpoem · Answer

Ok.

dan815 · Answer

dont think about the decreasing its just a mirror and repeated

trojanpoem · Answer

Yeah, you just turn left to right and so on.

dan815 · Answer

okay umm wait this is important first

dan815 · Answer

if u look at the 10 digit case

dan815 · Answer

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