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If we supposeA+B=2, A+C=4, B+C=8 thenGaussian elimination gives A=-1, B=3, C=5. The only restriction(other than the obvious observation that the sums must also be distinct) is that the sums must a...
#2: Post edited
<details><summary>If we suppose</summary>A+B=2, A+C=4, B+C=8</details> <details><summary>then</summary>Gaussian elimination gives A=-1, B=3, C=5.</details>
- <details><summary>If we suppose</summary>A+B=2, A+C=4, B+C=8</details> <details><summary>then</summary>Gaussian elimination gives A=-1, B=3, C=5.</details>
- <details><summary>The only restriction</summary>(other than the obvious observation that the sums must also be distinct) is that the sums must all be even. Perhaps the intention was that people would assume that any solution can be divided down to a case when the smallest sum is 1 and would then conclude that it is unsolvable?</details>
