{--
From the Mensa Genius Quiz-a-Day Book by Dr. Abbie F. Salny

Problem for April 7th:

"You are decorating for Spring," the problem begins, and I'm like: I am?

Dr. Salny responds: "CHUT UP, FOO'! AND READ THE PROBLEM!"

Okay, then!

You are decorating for Spring, and you've found a bargain: a huge box of 
beautiful decorated tiles, ...

... [see what she did with that? 'decorating for Spring' and 'decorated tiles'?]

... enough to provide a border in two rooms. You really can't figure out how to
arrange them, however. If you set a border of two tiles all around, there's one
left over; if you set three tiles all around, or four, or five, or six, there's
still one tile left over.* Finally, you try a block of seven tiles for each 
corner, and you come out even.

What is the smallest number of tiles you could have to get this result?

* OCD much? Is it me, or would I just throw away the one extra tile, seeing that
I had bought it at a bargain, anyway, and what's one tile between friends, 
seeing that I have a huge box of them, anyway?**

** two 'seeing's and two 'anyway's. OCD much, geophf?

Why, yes. Why do you ask?

ANYWAY!

MODULAR FORMS! Did you know that education in basic mathematics in Japan besides
addition, subtraction, multiplication and division includes the modulus as a
basic operator? So this problem should be a breeze for our Japanese Haskellers.

So, solve this problem.

First we need to know what the equations are.
--}

twoTiles, threeTiles, fourTiles, fiveTiles, sixTiles, sevenTiles :: Int -> Int
twoTiles   = ntiles 2
twoTiles, threeTiles, fourTiles, fiveTiles, sixTiles, sevenTiles :: Int -> Int
twoTiles   = ntiles 2
twoTiles   = ntiles 2