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# Sum of four distinct integers

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Intern
Joined: 08 Dec 2017
Posts: 40
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Kudos [?]: 42 [0], given: 70

Sum of four distinct integers [#permalink]  27 Nov 2018, 01:33
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
How many ways can we find 18 as a sum of four distinct integers?

Edit: positive integers should be counted.

Last edited by YMAkib on 29 Nov 2018, 13:21, edited 1 time in total.
Intern
Joined: 21 Nov 2018
Posts: 21
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Kudos [?]: 2 [0], given: 1

Re: Sum of four distinct integers [#permalink]  28 Nov 2018, 10:59
12
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
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Kudos [?]: 111 [0], given: 4

Re: Sum of four distinct integers [#permalink]  29 Nov 2018, 05:12
Expert's post
YMAkib wrote:
How many ways can we find 18 as a sum of four distinct integers?

Incorrect question..
four distinct integers would also mean negative integers and then there will be infinite solutions..
example -12345 + 12345 + 0 + 18 or -1+1+0+18 or 17+1+2+(-2) and so on
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern
Joined: 08 Dec 2017
Posts: 40
Followers: 1

Kudos [?]: 42 [0], given: 70

Re: Sum of four distinct integers [#permalink]  29 Nov 2018, 13:21
Edited the question.
Manager
Joined: 01 Nov 2018
Posts: 87
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Kudos [?]: 43 [0], given: 22

Re: Sum of four distinct integers [#permalink]  06 Jan 2019, 22:51
Expert's post
kunalkmr62 wrote:
12

Just in case you were not guessing, here's why that's not true.

here are 12 possible combinations
0,1,2,15
0,1,3,14
0,1,4,13
0,1,5,12
0,1,6,11
0,1,7,10
0,1,8,9
0,2,3,13
0,2,4,12
0,2,5,11
0,2,6,10
0,2,7,9
............. And we can keep going. 12 is not the solution.
Re: Sum of four distinct integers   [#permalink] 06 Jan 2019, 22:51
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