0 votes 0 votes The number of integers between 1 and 1000 inclusive have a sum of digits equal to 10 is_______ iita asked Jan 24, 2017 iita 1.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 2 votes 2 votes The number of solutions to a + b + c = 10 in non-negative integers is 12 * 11 / 2 = 66. From this list we must exclude the solutions in which one of the variables is 10. There are three such solutions, so 63 solutions remain. Tendua answered Jan 24, 2017 • selected Jan 25, 2017 by Sushant Gokhale Tendua comment Share Follow See all 13 Comments See all 13 13 Comments reply Tendua commented Jan 24, 2017 reply Follow Share Have you even read the answer before commenting. ? do you have a digit called 10 in decimal number system? only digits are 1-9 so the solution like 10 0 0 , 0 10 0 , 0 0 10 also make sum 10 these must be excluded 1 votes 1 votes iita commented Jan 24, 2017 reply Follow Share @Tendua what does it mean by "one of the variables is 10" as we are summing up only the digits.....??? 0 votes 0 votes iita commented Jan 24, 2017 reply Follow Share got it thanx buddy for help.. 0 votes 0 votes mcjoshi commented Jan 24, 2017 reply Follow Share @Tendua Bro, Sorry I didn't read question properly. (misunderstood) 0 votes 0 votes Rahul Jain25 commented Jan 24, 2017 reply Follow Share @ tendua how did you get 12×11/2??? 0 votes 0 votes iita commented Jan 24, 2017 reply Follow Share It's V(3,10) placing 10 digits in 3 places V(3,10)=C(12,10)=C(12,2) 1 votes 1 votes Rahul Jain25 commented Jan 24, 2017 reply Follow Share Thanks buddy. 0 votes 0 votes iita commented Jan 24, 2017 reply Follow Share but 10 0 0 will become a 4 digit number and in decimal why we have 0-9 so we are plcacing these 10 digits in 3 places if we will count 10 also then it will be 11th digit... ??? 0 votes 0 votes Prajwal Bhat commented Jan 25, 2017 reply Follow Share Tendua, You have considered 3 digit number i,;e a+b+c =10 but what if 4 digit number or even 5 digit number such as a+b+c+d=10 could you clarify this ? 0 votes 0 votes Tendua commented Jan 25, 2017 reply Follow Share @iita. This question can be viewed as the distribution of some object into boxes and my first comment was not correct. I just wanted you to read solution. So we have to make sum 10. Can be viewed as we have 3 boxed and have to distribute objects in such a way that sum become 10, It's formula is N+R-1 "C" R-1. Here R = 3 and N = 10. Now this will count every possible case and these cases also contain the cases where all the objects can get in one box. But actually we are considering digits in the form of objects and No such object like 10 exist in digits so we have to remove the cases where it is taking into consideration 10. @Prajwal bhatt. IF we have to also take in consideration the 4 digits numbers then we can in the same way extend it in the form of a+b+c+d =10. now r value = 4. 0 votes 0 votes Prajwal Bhat commented Jan 25, 2017 reply Follow Share My question was, here we just need to consider even 2 digits (Eg: 9+1=10 ) to till 9 digits (1+1+1.....+2=10) all those cases also should be considered right ? Correct me if i'm wrong! 0 votes 0 votes Tendua commented Jan 25, 2017 reply Follow Share Can't get what you asking but question say to only consider till 1000 so why will I take 5 digits into consideration and I have placed a box for every place place, for unit place for one for 10's place and ones for 1000 place, 1000 does not sum up to 10 so we have to consider the possibility till 0-999 0 votes 0 votes Prajwal Bhat commented Jan 25, 2017 reply Follow Share Yes got it i misunderstood the question now got cleared. Thanks 0 votes 0 votes Please log in or register to add a comment.