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# Icosahedron puzzle
Assume a regular icosahedron (20 sided polyhedron with triangle faces).
Assume 5 colors, Pink, Green, Blue, Orange, Yellow, that are each to be used 5 times as colors to edges of the shape.
Given the shape and colors, is it to make each vertex contain exactly one of each color?
## Example Diagram (unsuccessful attempt)
Each number to the left is a vertex
Each set to its right are its neighbor vertices
P G B O Y are colors Pink, Green, Blue, Orange, Yellow
Each pairing describes an edge, or a connection between vertices
This manual guesswork fails because it makes vertex eleven contain two Green points.
```
P G B O Y
01 { 02 03 04 05 06 }
P B O Y G
02 { 01 03 06 07 11 }
G B O P Y
03 { 01 02 04 07 08 }
B O Y P G
04 { 01 03 05 08 09 }
O Y P B G
05 { 01 04 06 09 10 }
Y O P B G
06 { 01 02 05 10 11 }
Y P
07 { 02 03 08 11 12 }
Y P
08 { 03 04 07 09 12 }
G B
09 { 04 05 08 10 12 }
G B
10 { 05 06 09 11 12 }
G G
11 { 02 06 07 10 12 }
12 { 07 08 09 10 11 }
```
## Purpose
This repo tries to "brute force" solve the puzzle.
It uses Elm as the implementation language.
## Example manual guesses
### After Blue
B
taken
V_01
V_02
V_03
V_04
V_05
V_06
V_07
V_08
V_09
V_10
V_11
V_12
need
```
[ EV_01 V_01 V_02 B
, EV_02 V_01 V_03
, EV_03 V_01 V_04
, EV_04 V_01 V_05
, EV_05 V_01 V_06
, EV_06 V_02 V_03
, EV_07 V_02 V_06
, EV_08 V_02 V_07
, EV_09 V_02 V_11
, EV_10 V_03 V_04 B
, EV_11 V_03 V_07
, EV_12 V_03 V_08
, EV_13 V_04 V_05
, EV_14 V_04 V_08
, EV_15 V_04 V_09
, EV_16 V_05 V_06 B
, EV_17 V_05 V_09
, EV_18 V_05 V_10
, EV_19 V_06 V_10
, EV_20 V_06 V_11
, EV_21 V_07 V_08 B
, EV_22 V_07 V_11
, EV_23 V_07 V_12
, EV_24 V_08 V_09
, EV_25 V_08 V_12
, EV_26 V_09 V_10 B
, EV_27 V_09 V_12
, EV_28 V_10 V_11
, EV_29 V_10 V_12
, EV_30 V_11 V_12 B
]
```
### After Blue, Yellow
Y
taken
V_01
V_03
V_02
V_06
V_04
V_05
V_10
V_12
V_08
V_09
V_07
V_11
need
```
[ EV_01 V_01 V_02 B
, EV_02 V_01 V_03 Y
, EV_03 V_01 V_04
, EV_04 V_01 V_05
, EV_05 V_01 V_06
, EV_06 V_02 V_03
, EV_07 V_02 V_06 Y
, EV_08 V_02 V_07
, EV_09 V_02 V_11
, EV_10 V_03 V_04 B
, EV_11 V_03 V_07
, EV_12 V_03 V_08
, EV_13 V_04 V_05 Y
, EV_14 V_04 V_08
, EV_15 V_04 V_09
, EV_16 V_05 V_06 B
, EV_17 V_05 V_09
, EV_18 V_05 V_10
, EV_19 V_06 V_10
, EV_20 V_06 V_11
, EV_21 V_07 V_08 B
, EV_22 V_07 V_11 Y
, EV_23 V_07 V_12
, EV_24 V_08 V_09 Y
, EV_25 V_08 V_12
, EV_26 V_09 V_10 B
, EV_27 V_09 V_12
, EV_28 V_10 V_11
, EV_29 V_10 V_12 Y
, EV_30 V_11 V_12 B
]
```
### After Blue, Yellow
O
taken
V_01
V_02
V_03
V_04
V_05
V_09
need
V_10
V_11
V_06
V_07
V_08
V_12
cant
06 10
```
[ EV_01 V_01 V_02 B
, EV_02 V_01 V_03 Y
, EV_03 V_01 V_04 O
, EV_04 V_01 V_05
, EV_05 V_01 V_06
, EV_06 V_02 V_03 O
, EV_07 V_02 V_06 Y
, EV_08 V_02 V_07
, EV_09 V_02 V_11
, EV_10 V_03 V_04 B
, EV_11 V_03 V_07
, EV_12 V_03 V_08
, EV_13 V_04 V_05 Y
, EV_14 V_04 V_08
, EV_15 V_04 V_09
, EV_16 V_05 V_06 B
, EV_17 V_05 V_09 O
, EV_18 V_05 V_10
, EV_19 V_06 V_10
, EV_20 V_06 V_11
, EV_21 V_07 V_08 B
, EV_22 V_07 V_11 Y
, EV_23 V_07 V_12
, EV_24 V_08 V_09 Y
, EV_25 V_08 V_12
, EV_26 V_09 V_10 B
, EV_27 V_09 V_12
, EV_28 V_10 V_11
, EV_29 V_10 V_12 Y
, EV_30 V_11 V_12 B
]
```