Department of Mathematics, Temple University, Philadelphia, PA 19122, USA.
Exclusive for the Personal Journal of S.B.Ekhad and D.Zeilberger.
Here is your chance to earn some extra Hannukkah GELT. Go for it! You might get some inspiration from my Maple package DREIDEL.
Added Oct. 30, 2003: Sujith Vijay and Thomas Robinson just solved the conjectures in this article. (Added Third Day of Hannukka (Dec. 22, 2003)): Read their intriguing proof
P.S.: Just in case you forgot how to play Dreidel: The k players take turns spinnig. They start out with NUTS nuts each, and immediately donate each one nut to the pot. If the dreidel landed on GIMEL the turner gets to take the whole (Ganze) pot, (and then everyone donates one nut to the pot). If it landed on Hay , the player gets the (smaller) Half (Halbe). If it landed on Nun, then the player gets Nothing (Nix), and if it landed on Shin, the player pays (Shalem) one nut to the pot.
Doron Zeilberger's List of Papers