Statement

Luca, Edoardo, William and Giorgio are playing at the famous card game briscola. While Edoardo was setting up the deck, he noticed that a card was missing. In fact, that same day he made a huge house of cards and he left the last card of his deck inside it! Now, he really wants to play with his friends without destroying his castle: help him find out how much of the castle must be torn down. An house of cards is made up of triangles of cards. If you remove a card that is under another, all the castle falls in pieces. You can easily remove a triangle from the top without risking a disaster, but you want to minimize the number of triangles removed to keep the structure beautiful. The card Edoardo wants is in the C-th triangle of the R-th row from the top of the castle, which has N rows total. Note that the i-th row (from 1 to N) has i triangles of cards. How many triangles of cards do you have to remove at least, in order to have the missing card in hand?