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Chamber 14 involves more momentum puzzles, as well as the puzzle of how to bring an energy pellet a long distance, around several corners.

The first challenge is to get hold of a cube to put on a button so that a door can be opened. This may sound straightforward, but the cube is on top of an unclimbable raised platform.

Getting the cube

The second portal at the bottom of the pit.
The first portal to fling towards the raised area.

Turn to the left and walk forward. As you do so, stairs will rise up, allowing you to simply walk to the pellet receiver. The cube is on your left. This is a momentum puzzle, as indicated by the fact that the stairs to the pellet receiver area retract once you're up there. Place the first portal high on the wall to the right of the raised area. Place another portal at the bottom of the pit formed when the stairs retracted, and fall into it. You should fly onto the raised platform.

The radio is located between the button and the door it powers, on the right wall. To reach it, place an orange portal just below the radio, and a blue portal on the high ceiling before the stairs. Drop through the orange portal and be ready to place another blue portal below you before you land. If you do this correctly, you will start to fly up and down repeatedly between the two portals. When coming out of the orange one, you should be able to grab the radio, and then adjust your path to stop moving through the portals. Bring the radio to the stationary platform in the middle of the sludge.
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The cube on the button.

Once you're on top of the raised area, you can pick up the cube and take it down to the button. As soon as the cube is off the raised platform, the stairs will permanently rise up again. Put the cube on the button and open the door.

If you do happen to at some point take the cube off of the button and move it any distance, the door will "malfunction" and become permanently open. This only happens after the cube is placed on the button, and is to prevent trapping yourself on the other side of the door.

Getting the pellet

An overview of the sludge area.

The door leads around a corridor to a room filled with sludge and some platforms which periodically go up and down into the sludge. On the other side of the room is a small antechamber with a pellet launcher; either use the platforms or a portal to get to the room.

The portal in the antechamber.

Once in the room, place a blue portal over the scorch mark on the wall, letting the pellet through. Now jump across the platforms and continue to the pellet receiver.

The portal above the pellet receiver.

At the pellet receiver, simply place an orange portal on the red spot above it – letting a pellet into it – and ride the lift below to the chamberlock.

Alternatively, before leaving the first room, fire a portal to the spot above the pellet receiver. Then walk across the platforms with the sludge and fire the alternate portal at the scorch mark.

Very, very good. A complimentary victory lift has been activated in the main chamber.

GLaDOS

Advanced

In the advanced chamber, a potential shortcut of flinging yourself onto the exit platform (see portals challenge, gold method) is prevented because the floor was made portal-proof. The box is also harder to reach due to more portal-proof surfaces, and the three platforms in the goo room are removed.

To reach the cube, you need to shoot a portal down the staircase and one next to the box section. Jump down, and you can maneuver yourself onto the box section. Place it as normal on the button.

To reach the pellet, you need to portal across the water area. Then place a blue portal on the scorch mark, and an orange portal back on the other side. Avoiding the pellet, walk all the way back to the main area, and place an orange portal above the pellet receiver. The exit lift will now lower.

Challenges

Portals

Bronze at 6 portals
  1. Blue portal on wall to fling towards cube.
  2. Orange portal at bottom of retracted stairs. Fling and grab the cube, placing it on the button.
  3. Blue portal across water gap.
  4. Orange portal in accessible location. Travel into pellet room.
  5. Blue portal on scorch mark. Travel by jumping or existing portals to main area.
  6. Orange portal above pellet receiver.
Silver at 4 portals
  1. Blue portal on wall to fling towards cube.
  2. Orange portal at bottom of retracted stairs. Fling and grab the cube, placing it on the button. Jump on platforms to cross the goo.
  3. Blue portal on scorch mark. Jump back across to the main area.
  4. Orange portal above pellet receiver.
Gold at 2 portals
  1. Blue portal on ground in front of the lift, as close as possible.
  2. Orange portal at bottom of retracted stairs. Jump in, and control your flight to land on the raised lift.

Steps

You can achieve bronze by using the pellet, but to get gold, you will have to use the shortcut route described in the 2-portal solution. You will use many more than two portals to do it, but that is the type of shortcut you should take.

Bronze at 55 steps
Silver at 20 steps
Gold at 10 steps

Time

Bronze at 50 seconds

Use a couple sets of portals to get up to the pellet receiver platform. Make sure you do not advance far enough at ground level to make the stairs rise, as this will waste time. Quickly place a portal and fall to fling to the cube. Place a portal to get close to the button and quickly get through the door. Portal on your side of the water, and another in the pellet room. Then one on the scorch mark, and come back through (alternately, peek-a-portal to save time). As soon as you can see it, place a portal above the receiver. Aim slightly above the red mark for a better chance to get your target. You can save some time waiting for the platform to lower and raise by grabbing the cube and standing on it, as you won’t have to wait as long to get onto the platform

Silver at 20 seconds

This award requires a method that flings you onto the platform while it is still raised. Portal yourself to the top of the stairs, and then place a portal in front of the lift and fling on through.

Gold at 10 seconds

Place an orange portal next to the lift, and a blue one right in front of the entrance elevator. As soon as you are through, place another blue one on the ceiling and go back through. Another blue one on the floor before you land, and maneuver yourself onto the lift and exit.

Alternately, there is a usable ceiling directly in front of the entrance elevator. Start an infinite fall, and you do not need to wait long before placing a portal in front of the exit lift. Maneuver yourself onto it, and exit for a time that can even be significantly below the gold goal.