Plastic tumblers or glasses can become stuck together if they are still wet when stacked, or if the glasses have been stacked together for a long period of time. Separating the tumblers may sound easy, but sometimes even brute force won't get them apart. A combination of ice and hot water often tackles the task when other techniques just don't work.
Hot and Cold Method
Fill the topmost glass with ice cubes, then run tap water until it's hot. Hold the stack at an angle under the running water so the hot water flows over the glass stuck to the top glass. Do your best not to get hot water in the top glass, as this could slow the process. Rotate the stack so all sides of the second glass get warmed by the hot water. Tug and twist gently to free the stuck glasses from one another. This process works by allowing the heated plastic to expand, while the chilled plastic contracts just enough to allow air between the two, which loosens the seal.
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If they still don't come apart, fill the sink with several inches of hot tap water, then place the stack in the sink. Fill the top glass with ice again, if the ice has melted. If the plasticware won't stay put, weigh it down with a heavy pot. Try loosening the stack again after 20 minutes or so. If the tap water doesn't get hot enough, heat the kettle and add some near-boiling water to the water already in the sink. Don't put your hands in the water if the water is extremely hot. Instead, use a dish towel to handle the wet stack.
Sometimes, a little oil can help unstick that stubborn stack of drinkware. Stack the glasses so the open end of one is on top. Drizzle a little cooking oil around the rim of the second glass from the top, aiming the oil so it can drip between the top two glasses. In a pinch, an oil-based salad dressing such as Italian or a vinaigrette will also work. If the tumblers are flexible, press the sides of the top one inward to help the oil get inside the second. Wiggle or twist the top tumbler to free it from the stack. Repeat the process with each remaining pair of stuck glasses, then wash them in warm, soapy water. Allow them to dry, unstacked, after rinsing.
To prevent plastic glasses from becoming stuck in the first place, dry each glass thoroughly before stacking it atop another. Stack them as loosely as possible without pressing down; this will make each tumbler easier to free from the stack when you need it.