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dan815
 one year ago
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
 one year ago
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

This Question is Closed

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Solve this in front of me. And give me another example

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay umm lemme show u why i think this relation is important one

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay ill show u all my work so far, its not much lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay 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
 one year ago
Best ResponseYou've already chosen the best response.1im looking at only the increasing case, and the decreasing case will be the same numbers

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1if 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
 one year ago
Best ResponseYou've already chosen the best response.1123 increasing 321 decreasing 456 inc 654 dec ( non bouncy) all )

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay now lets move to the 9 digit case

dan815
 one year ago
Best ResponseYou've already chosen the best response.1here is where we can see the pattern

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1123456789 987654321

dan815
 one year ago
Best ResponseYou've already chosen the best response.1leets only look at the increasing for now

dan815
 one year ago
Best ResponseYou've already chosen the best response.1dont think about the decreasing its just a mirror and repeated

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, you just turn left to right and so on.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay umm wait this is important first

dan815
 one year ago
Best ResponseYou've already chosen the best response.1if u look at the 10 digit case

dan815
 one year ago
Best ResponseYou've already chosen the best response.1there is 1 difference between all the digits,

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the sum of the difference have to add upto 9, and all of them have to be more than 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so u can see there is no way to arrange the 1s to get anything new that tells us there is infact only 1

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now if u look at the 9 digit, case we have 8 difference now there is a max number we can pick for the first place

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1What do you mean by all of them have to be more than 0 ? why not 0 ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1which is 1, not 0 anymore, but anything more than 1 means we will fail

dan815
 one year ago
Best ResponseYou've already chosen the best response.1because if the difference is 0 then we have 1 1 1 1 1 which is bouncy

dan815
 one year ago
Best ResponseYou've already chosen the best response.112345 all have diff 1 for their digits

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1You mean the difference between the numbers can't be zero. Fine I understood all.

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1The sum of difference 12345 is 4

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so for the 9 digit case we know that 1 is the biggest number

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now if you pick 1, then all the following differences have to be 1, so we know starting with 1 there is only 1 number 123456789

dan815
 one year ago
Best ResponseYou've already chosen the best response.1when you pick 1, the difference have to add up to 8 and we have 8 places so everything is 1

dan815
 one year ago
Best ResponseYou've already chosen the best response.1but when you pick 0, the differences can add up to 9 and we have 8 places

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1But if we used 2, won't the number above 23456789 will be bouncy if we added any other digit ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1yes that is why 2 is not possible

dan815
 one year ago
Best ResponseYou've already chosen the best response.1this is where the parition question starts

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Yeah. But you must give me 1 or 2 easy questions as not to lose the info I gained.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay i think we should just work on this simpler problem

dan815
 one year ago
Best ResponseYou've already chosen the best response.1a+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
 one year ago
Best ResponseYou've already chosen the best response.1a+b+c+d=7 how many solutions are there to this? where a<b<c<d

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Bouncy or non bouncy numbers ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1no this is just a separate question

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you have to find hte number of integer solutions to that equation

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Lol a = 0 , b = 1, c= 2 , d= 4 or a = 0 , b = 0 , c = 0 , d = 7 there is infinity. Clarify your aimbition

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1a = 4 ,b = 2, c = 1 ,d = 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you have to find the number* of integer solutions

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1a+ b = 2 , a < b < solve this.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1there is only 1 solution to that

dan815
 one year ago
Best ResponseYou've already chosen the best response.1oh and a b c d > 0 ofcourse

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Ok .. because only when a = 2 But what about this a + b + c = 50 a < b <c

dan815
 one year ago
Best ResponseYou've already chosen the best response.1yeah thats the question im asking u lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.150 is a big one try just 7 for now

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Ok a = 4, b = 2, c = 1, d = 0 (1) a = 5, b= 2, c =1 , d= =0 Maybe 2 or so

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i think a logical way to break this question down is to look at the differences

dan815
 one year ago
Best ResponseYou've already chosen the best response.1a+b+c=7 okay say a=0 this means we have a difference of 7 to distribute

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Ok , so failed because it doesn't satisfy the condition.

dan815
 one year ago
Best ResponseYou've already chosen the best response.10 , 1, 6 0,2,5 0,3,4 no other solutions with a = 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.1hmm okay u think about it for a bit, i am gonna look at something

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Damn _ I saw the condition a > b > c >d

dan815
 one year ago
Best ResponseYou've already chosen the best response.1thats okay too same thing

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1But In your solution you made a = 0 and other number = 0 this is not possible you have broken the condition right ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1xD dont get caught on details lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we need to work faster rn

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Lol, details is important. But what about a+b+c+d = 10^9 won't I die before completing it ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i found 11 increasing non bouncy numbers for digit 9 , im gonna work on 8 now

dan815
 one year ago
Best ResponseYou've already chosen the best response.1try this problem instead ditch the older one a + b+ c = 7 and a,b,c >0 and

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so we are allowing the equal case now

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Ok first a =0 b + c = 7 b = 0 c = 7 b =2 c = 5 b = 1 c = 6 b = 3 c = 4 b = 4 c = 3 b = 5 c = 2 b = 6 c = 1 Ok I got it , but still there is a lot a lot a lot of solutions

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1I got a scheme on how to do it first a = 0 b +c = 7 ( b from 0 to 7) and calculate c then a = 1 b+c = 6 (b from 0 to 6) and calculate c ... until the end.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1yes thats where i am right now

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now instead of this, people have found a formula to do that counting for the number of solutions

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1AND YOU LEFT ME CALCULATING !!!!!!!!!!!!!!!!! >:(

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1But at least I learnt the basics :P

dan815
 one year ago
Best ResponseYou've already chosen the best response.1this stuff is an intro to something called paritioning theorems in mathematics

dan815
 one year ago
Best ResponseYou've already chosen the best response.1people have been working on approximations formulas for this count

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1approximations ? So answers are not accurate ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the degree of error is quite low, so for the number we are dealing with the error will not effect it

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1What's that formula ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1in other words its like people are finding formulas that are able to solve higher and higher values for k a+b+c=k

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i dont know, there are a lot apparently

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay but theres still work to be done here before the formula

dan815
 one year ago
Best ResponseYou've already chosen the best response.1there are more simpler ways to count

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay like take this case for 9 digit

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the difference if you pick 0 as the start

dan815
 one year ago
Best ResponseYou've already chosen the best response.1are 1,1,1,1,1....,2 there is one of 2 that means there are 9 ways with a dfference of 2 and all 1s

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the other 2 cases are when all the differences are 1 which gives us 2 more cases so a total of 9

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now for the 8 digit case, we can use some combinatorics to count faster

dan815
 one year ago
Best ResponseYou've already chosen the best response.1for a starting value of 1 we have 8 cases for a starting value of 0 we can have a 3 somewhere or a 2 somewhere so 16 more ways from that

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1explain " there is one 2" we can have a 3 somewhere or a 2 somewhere

dan815
 one year ago
Best ResponseYou've already chosen the best response.1if u look at the differences

dan815
 one year ago
Best ResponseYou've already chosen the best response.1when u have 0 as a start

dan815
 one year ago
Best ResponseYou've already chosen the best response.1and we can have 2 and 2

dan815
 one year ago
Best ResponseYou've already chosen the best response.1how many ways to distribute 2, 2s in 8 positions

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1I am dumb lol. dw:1435693617081:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.1oops lol it should be 1 1, 2

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1And you didn't tell me where the 3 gone ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1no look at the differences

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we are trying to find the unique differences and see the number of permutatiosn each have

dan815
 one year ago
Best ResponseYou've already chosen the best response.1there is 1 way to arrange all 1s there are 8 ways to arrange one 2 and rest 1 there are 8 ways to arrange one 3 and rest 1 there are 8*7/2 ways to arrange two 2s and rest 1

dan815
 one year ago
Best ResponseYou've already chosen the best response.1and that completes the case for a=0 for the 8 digit case

dan815
 one year ago
Best ResponseYou've already chosen the best response.1for a=1 there are 8+1 way for a=2 there is 1 way so a total of 1+8+8+8*7/2+9+1= eight digit CASE

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so everything is basic computation including the combinatorics we can make computer do, the one part we need to figure out is the unique solutions

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Give me simple exercise

dan815
 one year ago
Best ResponseYou've already chosen the best response.1find a nice solution to that and we will solve this whole quetion in like 0.0000000000001 computation time hehe

dan815
 one year ago
Best ResponseYou've already chosen the best response.1a+b+c=5 a,b,c>0 Total number of solutions = ?

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1hahahahahahahahahaaaaaaaaaaaa, Nice solution ? I am using dumbs way.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1here is something that might be useful im not sure yet

dan815
 one year ago
Best ResponseYou've already chosen the best response.1if you take the 2nd differences we can allow 0 so this is great

dan815
 one year ago
Best ResponseYou've already chosen the best response.1then we can use a nice combinatorics trick

dan815
 one year ago
Best ResponseYou've already chosen the best response.1like look at this other question okay where we allow 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you can think of this problem like this think of the 10 as being 10 ones

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435694528337:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.11 1 1 1 1 1 1 1 1 1 and the number of places we can put 2 plus signs to get unique solution

dan815
 one year ago
Best ResponseYou've already chosen the best response.1will tell us total number of solutions

dan815
 one year ago
Best ResponseYou've already chosen the best response.11 1 1 1+ 1 1 1 1+ 1 1 this is saying 4 + 4 + 2

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Wait wait, here is my problem "put 2 signs to get unique solution"

dan815
 one year ago
Best ResponseYou've already chosen the best response.1there are a total of 12 spots if u count the 1s and + sign as spots so that means 12 choose 2 are the total number of integer solutiosn to a+b+c = 10

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1HAHAHAHA , I UNDERSTOOD Xd

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Give me example fast I understood xD

dan815
 one year ago
Best ResponseYou've already chosen the best response.1this is a useful result, now u can answer questions like say you and 2 friends have 10 dollars and only loonies allwoed now u know the total number of ways your money can be split

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1You were explaining to me combinations and permutations ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1or something with a huge solution but u can atleast get an expression for it, like a billion dollars is in a town of 10,000 people, you can now answer the total number of ways this money can be split between the people

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the solution to his, if its loonies must be

dan815
 one year ago
Best ResponseYou've already chosen the best response.1billion + 9999 choose 9999

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.11,000,000,000 P 10,000

dan815
 one year ago
Best ResponseYou've already chosen the best response.1but if u want to allow cents too then its ((billion*100 )+ 9999) choose 9999

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1But Permutations are right here ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1when we say chosoe and permute we are actually not thinking about permute and choosing

dan815
 one year ago
Best ResponseYou've already chosen the best response.1in your mind you know the formula you get and u just say was it a choose or permute

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1But how about the a+b+c+d = k ? I still can't think about it

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay so here is what im thinking about a way to solve this

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1When It was 7 you told me write them as 1111111 now 11+111+11 and calculate 2+3+2

dan815
 one year ago
Best ResponseYou've already chosen the best response.1wait i wanna work something out on paper first

dan815
 one year ago
Best ResponseYou've already chosen the best response.1hey man I think I found something very interseting :O but im not quitee sure yet what to do with it!! but taking a look at the 2nd difference is very very very very very interseting

dan815
 one year ago
Best ResponseYou've already chosen the best response.1I feeel like this will eventually lead to our own counting method for this whole thing

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1What did you find ? :>

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay okay look at this!! there is only 1 case we even need to lookat!

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay for example this one a+b+c=7 lets say and a,b,c>= 1

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now we consider the simplst case

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay now here is what we do

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now that 2nd difference can be solved with this method

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so there msut be 5 solutions to this

dan815
 one year ago
Best ResponseYou've already chosen the best response.1this gives us all the solutions for fixing first number

dan815
 one year ago
Best ResponseYou've already chosen the best response.1lets try a bigger example

dan815
 one year ago
Best ResponseYou've already chosen the best response.1i just need to deal with that first digit part lemme see about that one thing hmm

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1I must give you 100 medal for that work , awesome.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1this stuff is very interestin :D i feel like we found something very neat!

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Oh, before I forget. Dan are you good at partial integration ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay wait here is the bad part

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we solved a slightly different problem

dan815
 one year ago
Best ResponseYou've already chosen the best response.1lol because 112233 is still classified as a increasing lmao

dan815
 one year ago
Best ResponseYou've already chosen the best response.1but this is kind of good because we found this really cool relationship!

dan815
 one year ago
Best ResponseYou've already chosen the best response.1ill change that question and post it ON OS, let other ppl try it!
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