Problem 1286. MatCAT - Reconstruct X from Its X-rays

Created by Ned Gulley

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524 Solutions
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Last Solution submitted on Feb 03, 2023

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Alfonso Nieto-Castanon on 24 Feb 2013

regarding the discussion question, my guess is that the only cases where the answer becomes unique are those 'trivial' single-vector or equivalent cases. More precisely those cases where min(nnz(row_sums),nnz(col_sums))<=1. The reasons is that if one solution exist where x(a,b)>0 and x(c,d)>0 (and a~=c and b~=d; i.e. they are not in the same row or column), then you could simply subtract one from x(a,b) and x(c,d), and add one to x(c,b) and x(a,d), and the result will also be a valid solution... thoughts?

Andrea Caruso on 7 Nov 2020

Nice problem

锦 on 30 Jul 2022

good problem.

Armando Longobardi on 11 Nov 2022

See also this: https://it.mathworks.com/matlabcentral/cody/problems/47618

There is a nice video explaining how to solve these problems.

Solution Comments

Solution 6842954

1 Comment

1 Comment

Eric Le Saux on 4 May 2022

That's brilliant!

Solution 1215302

1 Comment

1 Comment

Shuvo Kumar Paul on 27 Jul 2021

Hello, I am a beginner. I tried a lot but couldn't figure out the solution. Can you please help me with this problem?

Solution 1191720

1 Comment

1 Comment

Andrew Newell on 18 May 2017

I confess, I found the results using intlinprog.

Solution 208042

2 Comments

2 Comments

Andrew Newell on 18 May 2017

I would love to know how you came up with that.

Daigo on 16 Jan 2022

I have no idea how you came up with this... So elegant.

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Problem 1286. MatCAT - Reconstruct X from Its X-rays

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Problem 1286. MatCAT - Reconstruct X from Its X-rays

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