When assembling a large jigsaw puzzle it is sometimes difficult to find space to do the work. Also if it is project of several days it is a problem to keep the puzzle on a table that has other requirements. If a sheet of something like hardboard in the dimensions of the puzzle is covered with the fuzzy cloth used to catch the burrs on velcro and each piece of the puzzle has on its back a dot of the velcro with hooks, the hardboard can be hung on a wall and the puzzle pieces can be placed on the board without taking up table space.
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Good idea, novel, and potentially asthetically pleasing. The backing might also use the magnetic sheet material and the puzzle be specifically made to fit on a refrigerator.