# 2048 Quiz Puzzle

This puzzle is based on the very popular game 2048, which was invented by Gabriele Cirulli, and (if you haven't seen it) details can be found here.

As you play the game you gradually end up with tiles of higher and higher values - 2, 4, 8, 16, and so on, up in powers of two to the 2048 tile which gives the game its name. And beyond to higher powers of two if you are good (and lucky) enough.

Every time two tiles combine you score the value of the resulting tile. So combining two 2 tiles to make a 4 tile will score 4.

To make an 8 tile you will have to make two 4 tiles (scoring 4 each) and combine them to make the 8 tile (scoring 8) which makes a total of 16. So combining tiles to make an 8 tile will score 16.

Can you find a general formula to calculate the score for any power of two? That is, to make a tile of 2 to the power x will produce a score of y.

Devotees of the game will have spotted that we are ignoring the fact that sometimes the new tiles are 4s and not 2s, and so the scoring would be a little different. However, for the purposes of this puzzle, we are keeping it simple and just working in 2s.

If you find the puzzle easy you can always extend it, assuming that one new tile in seven is a 4 not a 2!