Q. Is playing Scrabble allowed on Shabbos?
A. Poskim permit placing letters together on a board or similar and form words, when the letters are not fixed or attached to the board, or to each other, or when not being held together by a surrounding frame. (Shemiras Shabbos K’ 16: 23, Piskei Teshuvos 34: 16, quoting Igros Moshe O.H. 1:135 and Chaye Adam 37:6).
Ohr. Org – Ask the Rabbi 47, mentions: I showed Rabbi Chaim Pinchus Scheinberg, zt”l, an edition of Scrabble which had a flat board, without grooves for the tiles, and asked him if it is permitted to play this game on Shabbat. He acknowledged that some Poskim forbid it, and others permit it. He ruled that it is permitted, but that great care must be taken to ensure that the players do not forget that it’s Shabbat and write down their scores. A similar ruling is to be found in Thirty Nine Melochos p. 955.
Some Poskim consider Scrabble a kli shemelachto leisur since the game involves writing down the score. (Tiltulei Shabbos p. 24).
Horav Shlomo Miller’s Shlit’a opinion is to better avoid playing games that do not promote the kedusha of Shabbos.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a