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1. Keep it in your pocket
2. Hide it inside a chair leg
3. Bury in it your garden
4. Attach a weight to it and throw it over a pier into the ocean (use a fishing magnet to retrieve)
5. Surgically implant it in yourself
6. Surgically implant it in a volunteer
7. Use your bank's safe deposit box
8. Pay someone else to hide it for you
9. Hide it inside a notable artifact that's already in a museum
10. Hide it inside a public monument, so you know that it'll be safe over the duration
11. Decoy pen
12. Make a chest of drawers with a false bottom
13. Hide it in a regular chest of drawers, underneath all the clothes
14. Place it underneath the floorboards
15. Disassemble it and reassemble its components into non-pen objects then reassemble it later
16. Dissolve it in acid (a nobel prize winner once used this to hide their medal)
17. Invent thermos flasks, and once they are popularised hide the pen in the vacuum between the exterior wall and the interior wall
18. Sneak into a construction site, and bury the pen underneath drying concrete
19. Hide it in an attic
20. Hide it in a basement
21. Hde it inside a tree
22. Bury it underneath the ballast of a railway track
23. Dissasemble it into single-material components, and then surround each component with a block of identical material. Use as paperweights
24. Hide it in between the double walls of a house
25. Invent bin liners. Hide between a bin and its bin liner
26. Cut open a teddy bear, and hide inside
27. Make a plumbing-standard pipe, with a mesh at each end. Hide pen inside pipe. Insert into your plumbing system
28. Hide it inside a hat
29. Coat in precious metals, attach a chain, wear as jewelry
30. Hide inside a fake book
31. Hide inside skirting boards
32. Hide inside a door frame
33. Hide inside a door
34. Hide inside the barrel of a gun
35. Hide inside the shaft of a spear
36. Hide inside a rail on which curtains are mounted
37. Hide on top of a tall shelf to tall for the forces of evil to reach
38. Give it to a miner to hide inside a mine
39. Hide it inside a teacher's cane
40. Hide it inside a window pane
41. Hide it on the underside of a train (if the force of evil are blindly following magic einstein-pen-trackers this should throw them for a loop)
42. Sneak it onto a ship under construction, and hide it inside the material of the ship
43. Give to someone onboard a ship you know will sink on that voyage and whose wreck will not be investigated for the relevant duration
44. Hide it inside a corpse's burial clothes
45. Hide it inside a casket/coffin/whatever-is-the-correct-name-for-the-boxes-people-are-buried-in
46. Reveal myself to a government of my choice and explain the dilemma. Leave the hiding to them
47. Throw it up into a gap inside the ornaments on the roof of a historical building
48. Hide inside a walking stick
49. Disguise as a different type of pen. Gift to political leader (so it will be both safe and well-kept)
50. Hide inside a conductor's baton

A couple of times I found myself adding an 'honourable mentions' box, and then finding a way to include it in the main list ('Gift it to someone -> that's not exactly hiding it -> disguise it first' and 'Hide it underneath a bin liner -> bin liners weren't invented yet -> invent bin liners first'). I used some somewhat absurd solutions the previous two challenges, and inspired by the more down-to-earth answers of others so I tried to limit myself to the possible (nothing outside the technology range available to me, so no inventing AIs to do the job for me) although in the spirit of babble I generally tried to make every idea somewhat workable.

1. Pick the lock
2. Smash down the door
3. Unscrew the door from its hinges and remove it
4. Escape through a vent
5. Hack the door
6. Alter your administration records to show that you ought to be released
7. Wait 10 years for natural administration changes to destabilise your holders until it is no longer remembered that you should be kept here
8. Use a significant portion of your 10 years of energy to create an explosion that destroys the walls
9. Walk out between the comically spaced bars
10. Bend the bars to allow you to escape
11. Dig into the wall and remove the bars from where they were mounted
12. Dig out through a tunnel
13. Smash through the wall
14. Dig through the wall
15. Dig through the ceiling
16. Bribe the guards
17. Persuade the guards
18. Seduce the guards
19. Use your phone to contact people outside to break you out (probably bribed)
20. Make your imprisonment a political thing, and then wait for administration change
21. Make your imprisonment a political thing, and then wait for your supporters to break you out
22. Write and publish a high-quality book series under a pseudonym using your real face, make yourself a prominent social figure, purchase a house remotely and pay someone to make it look lived-in, and then one day act as though you have suddenly been mistaken for someone else and kidnapped
23. Use the energy in your phone battery to create an explosion to destroy a wall
24. Wait for someone else to escape and let everyone else out
25. Use the energy in your phone battery to melt the bars
26. Use the energy in your phone battery to melt the door lock bolt
27. Hire someone outside to invent teleportation, and then teleport you out
28. Invent teleportation remotely using your phone to access lab assets, and then teleport yourself out
29. Create an AI on your phone to vastly improve the data gain from using your camera, use this to scan yourself, and use your phone to access lab assets outside and print an identical copy of yourself, and then terminate yourself
30. Create an AI on your phone, and then let it do the work of figuring out the rest of the plan
31. Figure out the resonant frequency of the door, and then use your phone to destroy it
32. Ditto, but for the walls
33. Ditto, but for the bars
34. Conquer the world remotely, and then let yourself out
35. Hack a 3D printer outside, print a robot, and then guide that robot to get you out
36. Hack the five most prominent social media websites, and guide the world towards freeing you (or your reference class)
37. Hack the five most prominent social media websites, and use your influence to dismantle the influence and property of the owners of where you are being kept
38. Buy the-place-where-you-are-being-kept, and then walk out as the owner
39. Smash though a window
40. Remove the window without breaking it, and then escape through the gap left
41. Look up the make and model of the lock on LPL's youtube channel, and pick it with the instructions provided
42. Reverse engineer the strange physics of your phone battery/yourself, and use this knowledge to escape in ways unfathomable to myself
43. Hack the military administration systems of a foreign country, and mislead an automated drone strike such that it destroys one wall of your room
44. Hack the military administration systems of a foreign country, and edit yourself in as an informant on their side who needs to be retrieved
45. Remotely edit the law such that it does not allow for you to be kept here, and then appeal your case
46. Hack into a rocket mid-flight, and control it such that it crashes into where you are being held
47. Hack a nearby chemicals processing plant, and cause an explosion that destroys a wall of your room
48. Appeal to the matrix controllers
49. Crowdsource ideas online
50. Identify a small but relatively resourceful group of people with an understanding of rationality and an interest in physics, hack an account that previously made a post on babbling, make a new post on escaping a locked room, and then reveal in the comments that the situation is real and the prize of an object unknown to physics (yourself and a phone of limitless battery) is also real, I'm being serious we might have a solution to entropy here and all you have to do is get mE OUT-

1. Saturn V rocket
2. SpaceX Starship
3. Shine a torch (the something you are sending is light photons)
4. Point a radioactive source towards the moon
5. Point a neutrino emitter
6. Send data by interfacing with the satelites around the moon
7. Invent teleportation, and then teleport there
8. Create a machine that can exactly copy your object and then destroy the 'original', use it to get the object to the moon, and then resolve the resulting dilemma about whether it's the 'same' object with your choice of counterargument
9. Space elevator
10. Just walk
11. Sit on a nuke, and then detonate it
12. Actually, just detonate a nuke anywhere in an atmosphere, and statistically speaking at least one air particle is likely to make it
13. Project Orion Battleship (possible overlap with previous two)
14. Jump really high
15. Make a seesaw, stand on one end, and have a heavy object fall from lunar orbit onto the other end
16. Climb a ladder
17. Ohvyq n gbjre bs onory, ohg fgbc jura vg ernpurf gur zbba
18. Decelerate the moon until it crashes into earth, so that everything on the earth is also on the moon
19. Wait for a quantum event of negligable probability to take it there
20. Promise someone £1 billion conditional on them getting the object to the moon
21. Use that one company whose thing is sending products to the moon so they can say that there's one of those products on the moon
22. Wait for someone else to attempt a lunar landing mission, and sneak the object onboard (fun fact: it's already been done with the lunar art museum https://www.youtube.com/watch?v=csInNn6pfT4)
23. Reclassify Earth as the moon
24. Reclassify anything reachable as the moon, and then place the object on that
25. Place the object on the Apollo lunar samples
26. Monorail
27. Regular rail
28. Rail, but with more than two rails
29. Use a plane to accelerate really fast in-atmophere, and use that momentum to get to the moon
30. Ditto, but with running
31. Cannon
32. Trebuchet
33. Catapult
34. Make something that disables Earth's relative gravitational field for an object, and turn it on at the right time
35. Accelerate really fast in a submarine, and use that momentum to get to the moon
36. Use a fishing rod to tether the moon, and reel it in until it's close enough
37. Use a fishing rod to tether the moon, and reel yourslef towards it
38. Use a fishing rod to tether another celestial body, and reel yourself towards it until you're in the path of the moon, then wait for it to arrive
39. Stand on a mirror that faces downwards, which rises upwards on a stream of photons bouncing between this mirror and another mirror on earth that faces skywards
40. Project Sea Dragon
41. A tower comprised of Delta-V stages
42. A space shuttle, with more stages
43. Make a bridge that spirals from earth to the moon, and then walk
44. Ditto, but with a road vehicle
45. Fold an A4 piece of paper 45 times, and then climb up the resulting stack
46. Climb up a rope
47. Climb up a fireman's pole, and then slide down the last fraction to the moon
48. Gather a large number of golf balls, and hit each one away from yourself to accelerate
49. Use a spray can

     50. SLS