CISRA Puzzle Competition 2007 - Solutions

This is the archive of the 2007 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

B.4 Circular Logic

Intuitive Leap: The "geographical transmission" is a map which wraps around, due to the toroidal (donut) shape of the planet.

There are 225 letters in the "geographical transmission". 255 is a square number - it's 15 x 15. If we rearrange the map into a 15 x 15 grid, we get:

```lrrnnnrbbbbrlll
lllrrnnrbbbbrll
lllllrrrbbbbbrl
lllllllcbbbbbbr
rlllllrrrbbbbbb
brlllrdrerbbbbb
bbrlrddreerbbbb
rrrcrrrcrrrcrrr
riiirsrbrartttr
trrirsrbrartttt
rrrrrcbbbcrrrrr
nnnnnrbbbrrrnnn
nnnnnrbbbrllrrn
rnnnnnrbbbrlllr
```

The annotation refers to six cities, and a number of roads. By noticing that there are 6 instances of the letter 'c', and many straightish lines marked 'r', we can rewrite the map to make it a bit clearer:

```l\_nnn\bbbb\lll
lll\_nn\bbbb\ll
lllll\_|bbbbb\l
lllllllCbbbbbb\
\lllll/|\bbbbbb
b\lll/d|e\bbbbb
bb\l/dd|ee\bbbb
---C---C---C---
iii\sss|aaa/\_i
_iii|s/b\a|ttt\
t\_i\s|b|a/tttt
-----CbbbC-----
nnnnn|bbb|\_nnn
nnnnn|bbb|ll\_n
_nnnnn\bbb\lll\
```

Toruses have an interesting property - they wrap around in two dimensions. If you go left or right you'll eventually end up back where you started, and the same is true if you go up or down, you'll passing through the 'hole' of the donut and end up where you started.

This is a clue that the map can be arranged such that its left and right edges wrap around, and its top and bottom edges also wrap around. By expanding the map in each direction, we can get a better look at what's happening:

```l\_nnn\bbbb\llll\_nnn\bbbb\llll\_nnn\bbbb\lll
lll\_nn\bbbb\lllll\_nn\bbbb\lllll\_nn\bbbb\ll
lllll\_|bbbbb\llllll\_|bbbbb\llllll\_|bbbbb\l
lllllllCbbbbbb\lllllllCbbbbbb\lllllllCbbbbbb\
\lllll/|\bbbbbb\lllll/|\bbbbbb\lllll/|\bbbbbb
b\lll/d|e\bbbbbb\lll/d|e\bbbbbb\lll/d|e\bbbbb
bb\l/dd|ee\bbbbbb\l/dd|ee\bbbbbb\l/dd|ee\bbbb
---C---C---C------C---C---C------C---C---C---
iii\sss|aaa/\_iiii\sss|aaa/\_iiii\sss|aaa/\_i
_iii|s/b\a|ttt\_iii|s/b\a|ttt\_iii|s/b\a|ttt\
t\_i\s|b|a/ttttt\_i\s|b|a/ttttt\_i\s|b|a/tttt
-----CbbbC----------CbbbC----------CbbbC-----
nnnnn|bbb|\_nnnnnnnn|bbb|\_nnnnnnnn|bbb|\_nnn
nnnnn|bbb|ll\_nnnnnn|bbb|ll\_nnnnnn|bbb|ll\_n
_nnnnn\bbb\lll\_nnnnn\bbb\lll\_nnnnn\bbb\lll\
l\_nnn\bbbb\llll\_nnn\bbbb\llll\_nnn\bbbb\lll
lll\_nn\bbbb\lllll\_nn\bbbb\lllll\_nn\bbbb\ll
lllll\_|bbbbb\llllll\_|bbbbb\llllll\_|bbbbb\l
lllllllCbbbbbb\lllllllCbbbbbb\lllllllCbbbbbb\
\lllll/|\bbbbbb\lllll/|\bbbbbb\lllll/|\bbbbbb
b\lll/d|e\bbbbbb\lll/d|e\bbbbbb\lll/d|e\bbbbb
bb\l/dd|ee\bbbbbb\l/dd|ee\bbbbbb\l/dd|ee\bbbb
---C---C---C------C---C---C------C---C---C---
iii\sss|aaa/\_iiii\sss|aaa/\_iiii\sss|aaa/\_i
_iii|s/b\a|ttt\_iii|s/b\a|ttt\_iii|s/b\a|ttt\
t\_i\s|b|a/ttttt\_i\s|b|a/ttttt\_i\s|b|a/tttt
-----CbbbC----------CbbbC----------CbbbC-----
nnnnn|bbb|\_nnnnnnnn|bbb|\_nnnnnnnn|bbb|\_nnn
nnnnn|bbb|ll\_nnnnnn|bbb|ll\_nnnnnn|bbb|ll\_n
_nnnnn\bbb\lll\_nnnnn\bbb\lll\_nnnnn\bbb\lll\
```

The annotation says that a seventh city was planned, along with six new roads linking it to the other cities. Region 'b' is the only region where a city could be placed, such that six roads can be can drawn which connect directly with each other city without crossing another road.

The annotation also mentions the six regions bordering the region we have identified as 'b'. The regions bordering 'b', going clockwise from the top, spell out the answer to the mystery: ALIENS.