Traveling problems

[size=3]The problem:
'There are N countries and K travel guides (N>=K). Each guide has a number of tourists from each country (that number is >=0). Travel guides are incorectly informed because each of them should have only tourists from one country and each country only one guide. The task is to distribute as less as possible tourists from one giude to another so that they can begin their tours (Some travel guides may not have any tourists).'

So, we have an KxN matrix filled with numbers of tourists.

I think the idea is to pick a number from each row (but no two of picked numbers are from same column - country) so the sum of the rest is minimal. I just don't have any idea how to do that. Please help!
If you have any better ideas please post! Thanks![/size]
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