# Six fearsome heros

A puzzle by Raphael Finkel.

Grobly Grizik is planning to write a novel fashioned after "Star Trek: The Next Generation". In this novel, six of the crew members compete both at Fizzbin and at three-dimensional chess. Each crew member gets two independent rankings for ability at these games, with 1 ranked lowest and 6 highest. Every crew member has a personal hero among the crew, and every crew member is afraid of some crew member. Everyone is the hero of somebody, and everyone is feared by somebody. Nobody either fears him/herself nor counts him/herself as a hero. Nobody fears his/her own hero. From the given clues, discover every crew member's ranking at Fizzbin and at three-dimensional chess, as well as whom he/she fears and whom he/she counts as a hero.

1. Geordi ranks 2 at three-dimensional chess.
2. Picard ranks two positions behind Troi at Fizzbin.
3. Troi is feared by the person Geordi fears.
4. Worf's hero ranks 3 times lower at three-dimensional chess than the crew member who is best at Fizzbin.
5. Picard's hero fears Geordi.
6. Data's hero is not Geordi.
7. Data is the hero of Riker's hero.
8. The person who is worst at Fizzbin is better than Troi at three-dimensional chess.
9. The person ranked number 3 at three-dimensional chess is ranked 4 positions higher than Data at Fizzbin.
10. Riker is feared by the person Picard fears and is the hero of Worf's hero.
11. Riker is ranked 2 lower at three-dimensional chess than the crew member ranked 2 at Fizzbin.

## Solution

```       crew       fears      fizzbin    hero       tdchess
========== ========== ========== ========== ==========
data       geordi     1          troi       4
geordi     picard     3          riker      2
picard     troi       2          data       5
riker      worf       5          picard     3
troi       riker      4          worf       1
worf       data       6          geordi     6
```