Measure in 1 1/2 inches from each end of the 18-inch side of an 18-by-25-inch piece of 3/4-inch plywood.
Scribe a semicircle that is an inch wide and 1/2 inch deep every half inch along the 18-inch edge, inside the 1 1/2-inch marks. There should be 10 semicircles.
Repeat on the 18-inch edge of a second piece of 18-by-25-inch plywood piece. Cut out the semicircles using a router on both pieces of 18-by-25-inch plywood.
Stand the two plywood pieces upright with the semicircle edges on top. Position two planks of 25-inch 1-by-4 lumber between the two pieces of plywood, flush with the top and either side of the plywood. From a top-down view, this creates a rectangle shape. There should be 1/2 inch between the edges of the lumber planks and the first semicircles along the top of the plywood.
Drill two pilot holes sized for 1 1/4-inch screws through the plywood into the ends of the 25-inch planks, and then secure the planks in position with 1 1/4-inch screws through the pilot holes.
Finish the table frame as well as 10 pieces of 1-by-28-inch dowel with the wood finish of your choice, and let dry.
Place dowels between the semicircles on the top of the table, and hang your newspapers over the dowel rods.