KEYS AND BOXES SOLUTION

(Comments are signalled by ";".)

1. goto box1
2. put down
   ; if box1 had only keys, then it now has keys + ? (Case A)
   ; if box1 had only ?, then it now has only ? (Case B)
3. goto door
4. pick up
   ; robot picks up red item
5. goto table
6. put down
   ; table only has one red item
7. goto box1
8. pick up
   ; Case A: if robot has picked ?, then box1 only has keys (Case A1)
   ;              if robot has picked key, then box1 has keys + ? (Case A2)
   ; Case B: robot has ?
9. goto door
10. put down
    ; Case A1: box1 has only keys, box2 has only ?, door has ?
    ; Case A2: box1 has keys + ?, box2 has only ?, door has key
    ; Case B: box1 has only ?, box 2 has only keys, door has ?
11. goto box1
12. pick up
    ; Case A1: robot has key
    ; Case A2: if robot picked ?, then box1 has only keys (Case A2.1)
    ;                if robot picked key, then box1 has keys + ? (Case A2.2)
    ; Case B: robot has ?
13. goto door
14. put down
    ; Case A1: door has key + ?
    ; Case A2.1: door has key + ?
    ; Case A2.2: door has 2 keys
    ; Case B: door has 2 ?
15. goto box2
16. pick up
    ; Case A1: robot has ?
    ; Case A2.1: robot has ?
    ; Case A2.2: robot has ?
    ; Case B: robot has key
17. goto door
18. put down
    ; Case A1: door has key + 2 ?
    ; Case A2.1: door has key + 2 ?
    ; Case A2.2: door has 2 keys + ?
    ; Case B: door has key + 2 ?
19. goto table
20. pick up
    ; robot has red item
21. goto outside
    ; since door has key in all 4 cases, robot can go outside with red object