I've iterated on the concept, and made a game you can play in the browser, Gridogram: instead of being random, for each day a grid of letters is created from a quote or phrase of some sort that relates to the day.
For example, here's a grid that contains the Y Combinator motto [1]:
E G I W
L H N A
P T M K
S O E P
An interesting challenge on the development side is figuring out whether a quote will fit in a grid, and creating it in a reasonable amount of time. A 5x5 grid is the biggest one I've made, and that has over 100 billion possible paths along which to fit the words. Sometimes the search never gets there, still working on it, and planning to write up the more interesting parts once I've fully wrapped my head around them.
Grateful to hear any thoughts on the game!
[1] "Make something people want"