# Towers Rules

### A brief guide

This is an example of a finished Towers puzzle. This puzzle borrows heavily from Sudoku puzzles, but also has some of it's own rules. Firstly, this is a 9x9 grid, so each row and column must contain the number 1-9 once and only once. If you have a 5x5 grid, then each row/column would have to contain the numbers 1-5.
A Towers puzzle also has clues on both sides, and top/bottom. The clues tell you how many 'towers' you can see if you were look from that point in to the puzzle. The number in each cell tells you the height of that tower. As an example, take the top row looking from the left, we have a clue of '4'. Looking in to the puzzle from that point we would see 1, 3, 7, 9 (i.e. four numbers/towers). The 2, 5, 8, 4, 6 would be hidden behind the higher numbers/towers before.
Take the left-most column from the top, we have to clue '5'. So, looking down that column we would be able to see 1, 2, 5, 8, 9 (i.e. 5 numbers/towers). The 7, 6, 3 and 4 would be obscured behind the higher numbers/towers before.
This is an example starting grid. The easiest place to start is with the '1' clues. This clue means you can only 'see' one tower from that side, the only way this can happen is if the first number is 7 (in this case the width/height of the grid, i.e. the highest number).
Because each row/column will have one '7' in it, you will always have 4 clues of the value '1'. It's a little unfortunate in this case that it has only given us 3 numbers we can enter, and not the full 4.
After this easy start, you normally have to resort to applying the rules and entering pencil marks. However, for this particular puzzle we can enter another number immediately.
Look at the row with the highlighted cell. We are looking for where to put the 6'. It can't go to the right of the '5' because that would leave a number lower than 5 to the left of the 5, and we wouldn't be able to satisfy the '3' clue on the left. The '6' can't go in the left-most cell because then that would give us a clue of '2' on the left, so it must go in the highlighted cell.
Look at the right-most column, the hilighted cell in particular. The clue at the bottom is a '2', so the highlighted cell must hide the two cells above it. Taking in to account the 5 in the row already, and the '1' in the column already, that cell must 6 or 4. It can't be a 3 because that would mean the two cells above would be a combination of 1 and 2, and we already have a 1 in that column.
We inspect interesting parts of the puzzle inserting pencil marks as we go until we are able to start inserting numbers. As the puzzle starts to fill, we can start applying more of the traiditional Sudoku techniques.