A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
How many four digit numbers are there such that the digits add up to 10 assuming that all digits are allowed to be zero?
 2 years ago
How many four digit numbers are there such that the digits add up to 10 assuming that all digits are allowed to be zero?

This Question is Closed

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1less than 9999 but more than 1000 :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.11117 1171 1711 7111 1126 1162 1261 1621 2611 1216 1612 2161 6121 6211 2116 6112 etc

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0A more mathematical approach, probably?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.01000A + 100B + 10C + D = 10 100A + 10B + C + D/10 = 1

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0if the number is ABCD ^

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1pfft, that is the most basic mathematical appraoach i know :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0I liked what @mathslover said, but that doesn't resolve it. Sorry for taking the medal back. :(

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.01000A + 100B + 10C + D = 10  (1) A + B/10 + C/100 + D/1000 = 1/100  (2)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0But we must have four equations, no?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0No problem :) Parth , thanks though..

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0I am going to subtract the above 2 eqns

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1its most likely a counting application with permutations since order matters

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1how many basic ways are there to define 4 digits that add up to ten, and then how many ways can each group be sorted thru

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Can we use combinatorics for this?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1combinatorics brings to mind the nCr stuff; i think the nPr stuff might be more applicable

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0sorry to correct what @mathslover is doing is a bit wrong /////// A+B+C+D=10 is the requirement///////////

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.11117; how many ways are there to permute this? 1126 how many ways? 1135 1144

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1we have to account for 0 i spose, which is added computations

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0OH yes @harsh314 thanks a lot

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.14+12+12+12 +things with zeros

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1118: stuff like 1180, 1108, 1018, but not 0118 127 136 145 19 28 37 46 55

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1so permute the 3 groups and times it by 3

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.11900, 1090, 1009 looks to be 3 times the 2 groups as well except for the 55 :) 5500, 5050, 5005 is just 3

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0This is very long. :

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Instead of bruteforce, can we try something simpler?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1this isnt brute force anymore, its refining

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Lemme check my method again

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Forget it . . . I think I must try it again :(

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1im to focused on my exam in 30 minutes to think thru this clearerer

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Parth, do you have answer of it ? ?

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0maybe closer the answer

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.084 numbers ... I think

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0I will put up soln here soon... just thinking of more no.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0can the digits repeat Parth?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Well, a number still has four digits if the digits repeat. :)

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0I found this on net : http://answers.yahoo.com/question/index?qid=20080330145752AA36Ac2 Now, I am thinking can we use this method to find the answerr?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0We can think of the ones with zeroes like this: three digit numbers that add up to 10 * 4! two digit numbers that add up to 10 * 4!/2 there can't be 3 or 4 zeroes.

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.05193 is the answer or am i wrong as usual

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Hey wait, did I mention that the first digit can be zero?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.11117 is unique, 4 11xy has 12, and there are 3 ways to chose xy, and no zero groups 4(1)+3(12) 118 is unique, there are 3 ways, and 3 zero groups 1xy has 6 ways, and there are 4 ways to choose xy, and 3 zero groups 3(3)+3(6(4)) 55 is unique, theee is ony 1 way, and 3 zero groups xy 2 ways, there are 4 ways to choose xy, and 3 zero groups 3(1) + 3(2(4)) is there a flaw here?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Oh! Is it allowed to have 0910 as the number ?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1the first digit cant be zero and it still be a 4digit number tho

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0no but a number with first digit as 0 does not make sense look at my answer plz i think it is right

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0^ yeah after that 0910 is not a four digit number , it will be three digit number ..

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1have fun, i gotta run ;)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0I know... the question is making such an assumption, so...

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0well there can't be more than 186 numbers.. I think.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0yes it is 186 @ParthKohli

Meepi
 2 years ago
Best ResponseYou've already chosen the best response.2(0..9).each do a (0..9).each do b (0..9).each do c (0..9).each do d count = count + 1 if (a + b + c + d) == 10 end end end end puts count gave me 282 as answer, I don't know a mathematical approach though :)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0186 when 0 is allowed or not?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0282 and 186 are both not right :

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0i think i got the answer.............

Meepi
 2 years ago
Best ResponseYou've already chosen the best response.2282 was with leading zeros, without it would be 219

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0plz do reply if wrong.......

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0yes i got this too a silly error how did you do it............

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0my method is tooo long.......

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0... 286 is the answer

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0i too got the same but by long method how did you get it .........

Meepi
 2 years ago
Best ResponseYou've already chosen the best response.2I still find it odd that my bruteforce method which calculates the sum of the digits from 0 upto 9999 is off by 4

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0We wanted the number of non negative numbers \(a_1,a_2,a_3,a_4\) such that \(a_1 + a_2 + a_3 + a_4 = 10\). A formula says that it would be \(\binom{10 + 4  1}{4  1}\)

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0oh so no logic behind it as such..............

Meepi
 2 years ago
Best ResponseYou've already chosen the best response.2But bruteforcing every digit from 0 to 9999 gives 282 though, shouldn't they be the same?

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0my method was long and a bit calculation mistake.............. case1:::'1" as the first digit ,,,,,, the following subcases arise (a) .....with 2 zeroes ........9 has to be the sum of the remaining three numbers so total possible combinations are 3. (b) .......with 1 zero we have 810,720,630,540......all these have 6 combinations each so total 24 (c) .......with no zeroes.....711(3combinations),621(6),531(6),522(3),432(6),441(3),333(1) so total of 28 combinations hence for the 1st case we have 45 combinations similarly we can have others tooo..........and then add all........we get 286

harsh314
 2 years ago
Best ResponseYou've already chosen the best response.0but it would be great if any einstein of the present century could explain how @ParthKohli 's method came into being.............

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1works in google chrome :) <html> <body> <input type=button value="AddUp" onClick="qwe()"><br> 0000: <input id="txtOut0"><br> 1000: <input id="txtOut1"> </body> <script language=javascript> var a=0,b=0,c=0,d=0 var count=0 function qwe() {for (var x=1000; x<=10000; x=x+1) {if (a+b+c+d == 10){count=count+1} d=d+1; if (d>10) {d=0; c=c+1} if (c>10){c=0; b=b+1} if (b>10){b=0; a=a+1} if (a >9){x=10001} } document.getElementById("txtOut0").value=count //resets a=1,b=0,c=0,d=0, count=0 for (var x=1000; x<=10000; x=x+1) {if (a+b+c+d == 10){count=count+1} d=d+1; if (d>10) {d=0; c=c+1} if (c>10){c=0; b=b+1} if (b>10){b=0; a=a+1} if (a >9){x=10001} } document.getElementById("txtOut1").value=count } </script> </html>

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1i should prolly include an output such that we can verify its a+b+c+d parts to make sure its operating as expected

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1gotta weed out a bug :) 0,0,0,10 0,0,1,9 0,0,2,8 0,0,3,7 0,0,4,6 0,0,5,5 0,0,6,4 0,0,7,3 0,0,8,2 0,0,9,1 0,0,10,0 0,1,0,9 0,1,1,8

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1if abcd = 10 then reset to 0, not if greater than 10 .... lol

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1im missing 9001, 9010, 9100 from the end of my 0xxx for some reason 279+3 = 282 otherwise its 219 if we use actual 4digit numbers :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1... brute math, the easy way :)

Meepi
 2 years ago
Best ResponseYou've already chosen the best response.2Computers made these problem a lot easier :)

Meepi
 2 years ago
Best ResponseYou've already chosen the best response.2Unfortunately Parth has 286 as answer though :(

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1parth is counting somethings more than once then. i adjusted my loops to 0 to 10000 and it caught the last 3 ;)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.