It depends.
If we assume that:
-The density of the blocks is bigger than the density of the water.
-The epiphany of the top layer of bricks is the same as (or just not too larger than) the epiphany of the bottom of the barge
-The lake is pretty big so the water surface won't go higher/lower when we put/remove the block layer
Then they should put another layer of blocks on the boat. (and not remove a layer of blocks, since this would highen the barge).
At the picture it is clear that the two epiphanies are about the same (which makes me wonder how does the barge floats, but never mind that).
We know that the mass of water that gets displaced after we put the new layer of blocks, is the same as the extra mass of the barge after we place the new layer of blocks, and the volume of the displaced water is the same as the volume of the barge with blocks that sunk underwater. ( V(displaced water)=V(barge that sunk underwater) )
We know that the density of the bricks is bigger that the density of the water.
So lets say p(extra blocks)>p(displaced water) <=> m(blocks)/V(blocks)>m(water)/V(water) but m(blocks)=m(water), so:
<=>...<=>V(blocks)<V(water) so the volume of the extra blocks is smaller that the volume of the barge that sunk underwater, and because V(water)=V(barge that sunk underwater) we have
V(blocks)<V(barge that sunk underwater)
If A is the epiphany (surface) of the barge AND the epiphany of the top layer of blocks, then we have:
A*(new layer blocks height)<A*(additional sunk length) or blocks height<additional sunk length so blocks additional height is smaller than the additional sunk length. The barge with blocks will be lower and pass safely.
Using the same method you must prove that if you remove on layer of blocks, the barge with be higher and won't be able to pass. (try to do it yourself and tell me if you didn't understand something)
I hope it's not too complicated...
Note that this method may not be the best, but it is correct.
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