Deb - That is an attractive and functional idea!
May I make a suggestion ... try using the foam or vinyl poster board instead of cardboard. (I have gotten them at the Dollar Tree store for a buck a sheet.) And then use construction adhesive to attach the pennies to the vinyl/foam board. That will make it weather proof so that it lasts a long time. I love how it looks! Very fancy necklace for around the plants! If you don't have a large enough bowl to trace out the pattern, try using a thumb tac in the center with a string attached to the center and use a pencil (attached to the end of the string) to draw the first circle, then lengthen the string to make the outer edge of this necklace.
Your idea of cardboard would work for a short time until the cardboard decomposed. I don't know if Elmer's glue would hold up to water from rain or hose/sprinkler watering. I'd make one or two or three to last as the design looks like it would indeed deter slugs!
Do let us know how it works against slug attacks. I'd be interested to know your results.
