1 Cart, Rod 1

Beamcaster · Gem · Gem slot · Beam source ×4
6 puzzles on the surface layer, 4 with solutions. Heroes: Beamcaster.
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Beamcaster · Gem · Gem slot · Beam source ×4

Beamcaster · Boulder ×7 · Gem · Gem slot · Beam source

Beamcaster · Cart · Boulder ×2
Pieces that end up somewhere new: the cart and one of the 2 blocks. 2 other pieces stay where they start.

Beamcaster · Cart · Gem slot · Gem · Beam source · Boulder · Gate
Pieces that end up somewhere new: the cart, the gem, the beamcaster and the block. 1 other piece stays where it starts.

Beamcaster · Gem slot ×5 · Cart ×4 · Beam source ×8 · Boulder ×15 · Gem ×5
Pieces that end up somewhere new: all 4 carts, 2 of the 8 beamcasters and 2 of the 5 gems. 24 other pieces stay where they start.
Start: move the left cart right, push the left cart down and push the bottom left cart right.

Beamcaster · Cart ×3 · Beam source ×6 · Gem slot ×4 · Gem ×3
Pieces that end up somewhere new: all 3 carts, one of the 6 beamcasters and all 3 gems. 5 other pieces stay where they start.
Start: push the top left cart up 2 tiles, push the middle cart up 2 tiles and move the bottom left cart right.