Hi, 

I read the analysis of the '
https://codingcompetitions.withgoogle.com/codejam/round/000000000019fd27/0000000000209aa0',
 
and it said you can fill each row greedily, but it doesn't work for some 
cases.

Case 1)
N=4, K=10 and A=1, B=2, C=3, 
I filled the first row like below,
  1   4   3   2
  0   1   0   0
  0   0   2   0
  0   0   0   3 
(0 means an unfiled cell)
But it cannot be filled correctly because both colum 3 and 4 should have 
filled with 4. 

Case 2)
N=5, K=7, and A=1, B=2, C=2, 
If filled the trace like,  
  1   5   2   4   3
  2   1   5   3   4
  0   0   1   0   0
  0   0   0   2   0
  0   0   0   0   2
It either cannot be filled correctly because both colum 4 and 5 should have 
filled with 5. 

When I filled a trace reversely - like CBAA...A - it works well. Is there 
any condition that I missed?
And also, I couldn't prove the last part of the solution which Hall's 
Marriage is used for. If any hint or proof of it, I would appreciate. 

Thank you! 
Myeongchan

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