Problem Description

Number Puzzle
You are playing a puzzle game on an N*N grid. The aim of the puzzle is to place square tiles onto the grid such that their edges match. A tile consists of 4 numbers from 0 to C, inclusive - one number on each edge. All tiles are placed in a queue hidden from your view. The first T tiles are added to your hand. Each turn you can either:

1. Discard a tile from your hand (assuming you have discards left). The discarded tile will go to the end of the tile queue. OR

2. Place a tile from your hand into an empty cell on the grid. If two adjacent tiles have the same number k on their shared edge then you will receive k*k*k points.

After that you will receive the next tile from the queue, replacing the recently discarded/placed tile in your hand. Once the queue is empty then you will receive no more tiles. The puzzle is completed once all the tiles have been placed on the grid. Your task is to score as many points as possible.

Problem Setter: dimkadimon
Problem Testers: JacoCronje and nika