Logic Masters Deutschland e.V.

Rules:

Draw three paths, one red, one blue, and one green, which collectively visit all cells.
Each path starts at the "S" which matches its color and ends at the "G" of the same color.
Paths cannot branch, nor cross themselves, but may cross each other.
Paths cannot turn at crossings, and cannot otherwise overlap.
Paths cannot cross at cells containing a number or a black triangle (elevator).

Each path starts on floor 1 and can only transition between floor numbers at an elevator.
Paths can only cross when they are on different floor numbers (see below).

A cell containing a "+" symbol is a given crossing. Which paths cross there, must be determined by the solver.

A cell containing an upward pointing black triangle is an up elevator.
A cell containing an downward pointing black triangle is a down elevator.
A path entering an elevator transitions one or more floors in the indicated direction (up/down).

A path cannot exit an elevator on the same floor it entered - the floor number must change.
A path already on the highest floor, 4, cannot enter an up elevator.
A path already on the lowest floor, 1, cannot enter a down elevator.

A cell containing a number, N, indicates both a floor number and a region visit number.
A path may only enter that cell when it is on the Nth floor, and during its Nth visit to the region.

On a path's Nth visit to a region, the path must pass through exactly one cell containing the digit N before exiting the region.
Elevators may be entered before or after entering the region to attain the appropriate floor number.

The segment leading away from a paths starting point, "S", counts as the first visit to its starting region, so it must pass trough a 1 before leaving the region. Likewise, it must pass through the number corresponding to its last visit on its way to the "G".

Between elevators, a path must either pass through a numbered cell, or cross one or more other paths, or both.

Note that in the case where a path does not pass through a numbered cell between elevator trips, it must take the lowest numbered floor consistent with the elevator directions and all the crossings along that segment. (With this rule, in this puzzle, it will always be possible to determine which path at a crossing is on the higher floor.)

For answer check (penpa only): use green lines for all paths, but color each path using the Surface tool (Red, Green, Blue). On crossings, use the color of the path on the higher floor.

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