# Letter Counts in Ex Libris

In the board game *Ex Libris* one draws cards with book shelves and has to arrange them in alphabetic order. The catch is that one can only rarely rearrange the cards that one has put down onto the table. Also one gets extra points for the largest rectangular section. There can at most be three rows of shelves. Therefore one should try to have a third of the alphabet in each row. But where should one separate?

Helpfully they have given the number of shelves per letter on the summary card. One can see the counts here:

Using this one can make a cumulative sum and then plot this again with lines indicating the three thirds of the cards available:

We can see that the first row should be A to G, then H to P and then Q to Z. This will make it slightly easier to play the game, I hope!