A 220 × 260 cm room, a single bed (110 × 200) and a desk (105 × 50). The planner outlines both in red. Here's why, by hand.
Step 1: area
Bed 110 × 200 = 2.2 m²
Desk 105 × 50 = 0.525 m²
Total 2.725 m² → 47.6% of the room
More than half the floor is free. Area alone gives no reason to expect a clash.
Step 2: overlap
Compare horizontal and vertical ranges separately. Both have to overlap for the rectangles to collide.
Vertical bed 10–210 · desk 15–65 → 50 cm
Overlap 7 × 50 = 350 cm² = 0.035 m²
In practice: the desk hits the bed frame and can't go flush against the wall. The planner's furniture total also counts that 0.035 m² twice.
Step 3: can the desk slide over?
Needed 7 cm → 5 cm short
No. Pushing the bed flat against the left wall frees 10 cm instead, leaving 3 cm between bed and desk. That clears the overlap.
Step 4: the doorway
Rule must also be more than 30 cm from the bed → foot of bed at y ≤ 200
Now foot of bed at y = 210 → 10 cm short
So the route was blocked before it began. Pushing the bed up against the top wall as well gains the missing 10 cm.
Turn the desk 90° onto the right wall and there's 60 cm between them and a route from door to back.
At this size, one centimeter changes the answer. Measure along the floor, baseboard face to baseboard face.