# Solution to Numeracy

Each number in the list is to be converted into a base b, b = 2 through 10, with each base being used only once. Once in the appropriate base, the number will have a square number of digits, and the only characters will be 0 and b-1. The number of digits are as follows:

```(base b)^(# of digits in base b) = (# of digits in base 10)
2^361  = 112
3^225  = 113
4^196  = 122
5^169  = 119
6^169  = 132
7^144  = 121
8^144  = 131
9^121  = 116
10^121 = 121
```

Once in the appropriate base, the number can be arranged as a square to display some figure (each figure is given below). Each figure is a number in some writing system, all of which can be found at omniglot.com. The number the corresponds to a letter by a simple A=1, B=2, etc. substitution, and the ordering of the resulting letters to form the answer is given by the bases the original numbers were converted to:

```letter numeral base square size writing system
A      1       2    19x19       Financial Chinese
C      3       3    15x15	Javanese
A      1       4    14x14	Thai
D      4       5    13x13	Tibetan
E      5       6    13x13	Tengwar
M      13      7    12x12	Mayan
I      9       8    12x12	Lao
E      5       9    11x11	Arabic
S      19      10   11x11	D'ni
```

The figures are as follows (they all look better with a 1:1 aspect ratio, like you'd get using graph paper...):

base two:

```.........0.........
.........0......0..
.00000000000000000.
.........0.........
.....000000000.....
..0................
..0000000000000000.
..0.............0..
.0.............0...
.0...000000000.....
...................
.....000000000.....
.....0.......0.....
.....0.......0.....
.....000000000.....
.....0.0...0.0.....
........0.0........
........0.0........
0000000000000000000
```

base three:

```..0...0.0......
.0.0.0.0.0.000.
0..0.0.0.0.0.0.
0..0.....0.0.0.
0..0.....0.0.0.
0..0..0..0.0.0.
.0.00000.0.0.0.
.........0.0.0.
.....00000.0.0.
....0......0.0.
...0.......0.0.
...0.......0.0.
...0.......0.0.
....0.0000.0.0.
.....0...00..00
```

base four:

```.....0000......
...0.....000...
..0.........0..
.0...........0.
.0...........0.
0.............0
0....0000.....0
0....0..0.....0
.0...0..0.....0
.0...0000....0.
..0....0.......
..0....0.......
...0...0.......
....0000.......
```

base five:

```......00.....
....00.0.....
..00...0.....
00......0....
0........00..
0..........0.
.0...........
.0...........
..0..........
...00........
.....00......
.......00..0.
.........00..
```

base six:

```.0...........
.0...........
.0...........
.000000000000
.0...0.......
.0...0.......
.0...0.......
.0...0....0..
.0....0000...
..0..........
..0..........
...0....0....
....0000.....
```

base seven:

```............
.000.000.000
.000.000.000
.000.000.000
............
............
000000000000
000000000000
............
000000000000
000000000000
............
```

base eight:

```...000...0..
..0...0...0.
.0....0....0
.0....0....0
0.....0....0
0.....0....0
0.....0....0
0.....0....0
0.....0....0
000...0...0.
0.0...0...0.
000....000..
```

base nine:

```..0000000..
..0........
..0........
..0........
..00000....
.......0...
........0..
........0..
........0..
..0....0...
...0000....
```

base ten:

```...........
00000000000
.0.......0.
.0...00000.
.0...0...0.
.0...0...0.
.00..0..00.
.0.0.0.0.0.
.0..000..0.
00000000000
...........
```

2006 MIT Mystery Hunt