Introduction
Replacing a broken cable is easy when you can see the broken end in the shifter but it's impossible when you can't!
You'll try to downshift but after a couple of clicks, you won't be able to shift anymore.
Because you've not downshifted to can't remove the broken wire and bead.
This guide shows you how to make a hook to pull the ratchet allowing the gear to downshift.
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            I used 1.6mm green plastic-covered plant wire from Bunnings. The wire needs to be bendable and yet stiff enough to hold a hook. 
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            Strip the green plastic and bend the end 2mm 
 
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            Downshift as much as you can 
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            Pull the brake to open 
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            Insert the hook into the hole that the cable comes through, and then rotate it so that it holds where the cable bead normally sits 
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            Close the brake so the wire is loosely held 
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            Gently pull the wire while downshifting. You'll now be able to feel and hear the downshifting. Continue until it's fully downshifted 
 
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            Pull the brake lever and you'll now be able to pull the broken wire out with long nose pliars 
 
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To reassemble your device, follow these instructions in reverse order.