Judge's Notes on Bulletin Board

The last datasets are big, with 100 posters of large dimensions.  The last two are shuffled in a random order, but the set of entries follow a simple pattern making the answer easy to check.

One set has rectanges of width 49900 and height 39900 with corners at (0, 0), (1, 1), (2, 2), ... (99, 99)  leaving a region of area (49900-99)*(39900-99) = 1982129601 covered by all 100.   The clear space is in stairstep patterns in two corners plus the last row and column: 2*(1 + 2 + 3 + .... + 99) + 50000 + 40000 - 1 = 99899.

The next dataset is a regular rectangular 10*10 arrangement of 4999 by 3999 tiles overlapping  by 3 horizontally and 4 vertically, so there are 9*9 places where four overlap in a rectangle of area 3*4, for a total of 81*12 = 972.  Overall the tiles cover a large rectangle leaving clear 50000* 40000 - (10*4996 + 3)*(10*3995 + 4) =  3778298