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Place one end of each piece of scrap wood on the ground at an angle and have the opposite ends all meet over the top of the stump in a cone shape. This is a common method of assembling firewood over open flames to promote combustibility. You can also simply put the scrap wood on top of the tree stump. However, the stump may take longer to ignite this way. Use a match of kindling to light the scrap wood from the bottom. Do NOT use gas to light the scrap wood. The time it takes for a stump to catch on fire varies on a case-by-case basis. Allow up to 1 hour for the stump itself to ignite. Dry leaves, dry bark, and even dryer lint all make good kindling when starting a fire. Any dry, easily shredded material makes great kindling. Your stump will probably take several hours, or maybe even days, to completely burn. Add scrap wood to the fire as necessary to keep burning the stump until it's gone. You will most likely not have to add any wood to the fire for a small stump; the initial fire will probably be enough to burn the entire stump. If your stump takes more than a day to be removed through burning, add wood to the fire until midnight, then let it burn until the morning. The fire will weaken overnight but in all likelihood will not die out. As the stump smolders and the wood is turned to ash, keep an eye on the stump to make sure the fire is under control and doesn't need to be rekindled. Be ready to put out the fire with water or dirt if it begins to burn out of control or threaten to spread to the surrounding area. Schedule a hefty block of time in which to carry out your burning; the stump will probably take at least an hour or 2 to be removed.
Construct a teepee-like shape over the stump with scrap wood. Light the scrap wood and wait for the stump to ignite. Add more wood to keep the fire going as necessary. Monitor the stump until all the wood has been reduced to ash.