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From Alex in Huntingdon we have the following solution:

Dear Bernard,
I have thought of some solutions for Newspapers Challenge. I have named the pieces of paper A and B. A has numbers 1, 2, 7 and 8 on it. B has 3, 4, 5 and 6 on it. Here they are:

The solutions that start with A The solutions that start with B
1,2,3,4,5,6,7,8 3,4,1,2,7,8,5,6
1,2,5,6,3,4,7,8 3,4,7,8,1,2,5,6
1,2,7,8,3,4,5,6 3,4,5,6,1,2,7,8
1,2,7,8,5,6,3,4 3,4,5,6,7,8,1,2
7,8,3,4,5,6,1,2 5,6,1,2,7,8,3,4
7,8,5,6,3,4,1,2 5,6,7,8,1,2,3,4
7,8,1,2,3,4,5,6 5,6,3,4,1,2,7,8
7,8,1,2,5,6,3,4 5,6,3,4,7,8,1,2

I hope they're all right!