Question 1190980: if you add the digits in a number, how many numbers between 0 and 1000 will have a sum of 15?
Found 3 solutions by Alan3354, greenestamps, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! if you add the digits in a number, how many numbers between 0 and 1000 will have a sum of 15?
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I doubt there's an algebraic solution, so just list them and count them.
eg, there's 69,78,87,96,168, ... 951,960
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
Just "listing them and counting them", as the other tutor suggests, makes it easy to overlook some solutions or count some solutions more than once.
It is true that there is no (elementary) formal algebraic solution to the problem, so you need to make a list. But do it in an organized way to make sure you count each solution only once.
To make an organized list to find the answer to the problem, instead of listing each number that satisfies the conditions of the problem separately, list each COMBINATION of digits that satisfies the conditions, and determine how many different numbers can be formed with each of those combinations.
And in listing the combinations, make sure each entry in your list has the digits in non-decreasing order. For example, if you have "447" in your list, you don't want to have either "474" or "744" in the list also.
So here we go....
digits # of arrangements
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69 2
78 2
159 6
168 6
177 3
249 6
258 6
267 6
339 3
348 6
357 6
366 3
447 3
456 6
555 1
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65
ANSWER: 65
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As pointed out by tutor @ikleyn, my list is not complete -- it does not list 3-digit numbers containing 0 as a digit. To complete the list....
digits # of arrangements
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690 4
780 4
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ANSWER (final, corrected): 65+8=73
Answer by ikleyn(52855)  (Show Source):
You can put this solution on YOUR website! .
if you add the digits in a number, how many numbers between 0 and 1000 will have a sum of 15?
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In the solution by @greenestamps, the idea is correct,
but the list of possible numbers is not complete.
The three-digit numbers containing zero digit should be added
690, 609, 960, 906,
780, 708, 870, 807.
So, the total number of all possible three-digit numbers is 65 + 8 = 73.
ANSWER : 73.
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