Those apprenticed under Escher, Geisel, and Penrose never produce impossible structures. Those apprenticed under Johnson and Statmin always do. Self Taught architects sometimes do.

I couldn't find a reliable way of determining which Self-Taught architects would produce impossible structures, so I will have to go with four of D, E, G, H, K.

All the really cheap structures are made out of wood and dreams. Unfortunately none of the 5 architects proposals have these materials. Excluding these the next cheapest ones are all made out of 2 of wood/dreams/steel, the next set have Glass and one of the other 3, this suggests K will be cheapest. Silver is the next cheapest, so we want D, E and H.

My submission is therefore : D, E, H, K
 

There is some evidence that 2 artillery is sufficient to deal with 3 tyrants, but the amount of data is a bit small. I couldn't see any other change I could make which wouldn't lead to at least some measurable risk of loseing.  Risking being eaten to impress my superiors feels like a poor trade off, especially as they should hopefully be at least somewhat impressed with winning a battle at 10:16 odds, so I will stick with my initial selection. (Though I'm pretty sure that someone who was willing to take some risk of being eaten for extra prestige would be well advised to take one fewer artillery.)

 The more soldiers that come, the higher the chance of victory. We however will be outnumbered by at least 6, and previous squads that were outnumbered this badly only won 58 percent of the time.
 
There is no massive difference where the presence of one weapon and alien leads to victory, or where an alien is present but a weapon absent leads to defeat.

Looking at the cases where 1 soldier fought 1 alien:
- Artillery reliably win against venomopede, tyrants, scarab (only 8 records), crawlers, abominations
- Flamethrowers reliably beat crawlers, scarabs (only 5 records), normally win against venomopede, but normally lose to abominations, and consistently lose to tyrants.
- Grenades reliably win against abominations, crawlers, scarabs (only 6 records), venomopede normally win against tyrants 
- Lance reliably win against venomopede, scarab (only 6 records), crawlers, abominations normally win against tyrants
- Minigun reliably wins against crawlers, scarab (only 3 records), venomopede reliably loses against abominations, tyrants
- Phaser reliably wins against venomopede, scarab, crawler, normally wins against abomination reliably loses against tyrants
- Torpedoes reliably wins against abominations, crawlers, scarabs (Only 5 records), venomopede normally wins against tyrants
 
 Tyrants look like the strongest enemy followed by abominations.
 
When 1 soldier faced 2 abominations they always lost unless they either had torpedoes, lance or artillery. Torpedoes seem best but aren't perfect.
When 1 soldier faced 2 crawlers they always won if they were equipped with grenades, lance or phaser.
When 1 soldier faced 2 scarab they always won unless they were equipped with artillery or torpedoes.
When 1 soldier faced 2 tyrants they always lost unless they were equipped with artillery which won about half the time.
When 1 soldier faced 2 venomopedes they always won if they were equipped with grenades or lances

When 2 soldiers go into battle they are never equipped with the same weapons.
 
When 2 soldiers faced 3 tyrants the only combinations with victories were (torpedoes + mini gun and torpedoes + lance). 1 Artillery was insufficient. Suggest 1 artillery is insufficient to deal with 3 tyrants.
 

Looking at battles where only scarabs are present suggests the following limits on the number that can be defeated by a single type of weapon reliably:
- Artillery and tropedoes: 1
- Grenades and lances: 2
- Rifles and flamethrowers: 3
- Phasers: 4
- Minigun: 5

It looks like that if you have enough weapons to reliably win against each type individually then you will win reliavbly against the group.

This suggests that the following would give us a 100 percent - epsillon chance of victory:
- 3 artillery (Deals with Tyrants)
- 2 mini guns (Deals with Scarabs) 

- 3 torpedoes (Deals with Abominations)
- 1 grenade (Deals with crawlers/venompede)
- 1 lance (Deals with crawlers/venompede)

I suspect it can be done with fewer soldiers, however this is my provisional lineup if I don't get a chance to look at this further.
 

>!Grey turtles have a much lower weight than most 3.9->7.9
Greyish green turtles have a lower weight then the green ones, though the ranges overlap. Lowest 13 highest 42.9
There is a big spike in the number of green turtles with a weight of 20.4
Suggests we are dealing with multiple distinct species.

 
The spike in green turtles with a weight of 20.4 all have 6 shell segments. 
No green turtle with 6 shell segments has a weight other than 20.4.
Therefore Harold has a weight of 20.4

 
All gray turtles have fangs, and no other coloured turtles do. Means we can ignore this as any effect will be entirely contained in the colour.

There appears to be a slight increase in weight with the number of wrinkles, scars, shell segments, and miscellaneous abnormalities, though the rate of increase depends on shell colour, and to a lesser extent on nostril size.
 
Fitting a linear model explains just under 80 percent of the variation for grey turtles, and a little over 50 percent for the rest.
There is no obvious pattern to the deviations, and there is clearly a lot of randomness as a lot of identical turtles have widely differing weights.

My best estimate for the weights of the turtles based on the linear model is as follows:
Abigail      20.0
Bertrand     17.3
Chartreuse   22.8
Dontanien    19.2
Espera       16.5
Flint         6.8
Gunther      25.5
Harold       20.4
Irene        21.7
Jacqueline   18.6

If I wanted to maximise my income from the constitutional despot I should bump up the estimates a bit, however I don't need the money, and frankly my reputation as an honest scholar is worth more than a few gp. And who knows if enough people ignore perverse incentives like this he may stop offering them and become a less wrong constitutional despot? I can dream at least. As for the unflattering portrait, you can always judge someone by the quality of the pepole you have offended. Coming from him that is going to be seen as a compliment by the people that I care about, not an insult. So I will just give him my best estimates and move on.

Looking at this further, by far the strongest effect is the latitude, and that looks more like a rectangular effect than a trigonometric one. Replacing  the trigonometric fit with one that modelled a rectangulat latitude effect and no other yielded a model that explained most of the variation. By itself this looks better than the previous model.  

The next biggest effect looks like it is due to variation in murphys constant. This looked vaguely quadratic. 

The next biggest effect looked like it was due to variations in the value of Pi. It looked vaguely triangular, with the point ust below 3.15. 

The next biggest effect looked like a vaguely sinusoidal variation due to the longitude.

Including all of these in a model yielded one with a standard deviation of 4.9, and predicted that the following 12 locations were the best:

76804 VALUE:87.95301643603202
16965 VALUE:88.18566645580597
104815 VALUE:88.34280034001172
8415 VALUE:88.39346893009704
18123 VALUE:88.50303192064138
107929 VALUE:88.5221749787355
99595 VALUE:88.59004262250107
80395 VALUE:88.59313676878352
42742 VALUE:88.72736581213306
40639 VALUE:88.80584599223495
65607 VALUE:90.36919375244607
94304 VALUE:90.63981001558145

This is currently my best estimate. As the predicted values are all < 100 I will have to file a report on this with the empires colonisation department in case there is every any interest in making another attempt, but I won't risk the empresses' rath by attempting to colonise any of them.

Thank you for posting this. My findings are as follows:

Only 2 existing locations have > 100 performance. Both of these have:
- No strange smell
- Mint air
- Adequate Feng Shui

Most other high performers (But sub 100) have the same properties. Addittionally the weird sounds of the high performers are either:
- Eerie Silence
- Otherworldly Skittering

This suggests it would be sensible to restrict ourselve to locations with these properties. This alone increases the average performance from 23.12 to 46.92

High values of murphys constant are bad, though the affect seems to become small at around 3.5. There is some evidence to suggest that amongst the high performing section (But not the others) too low a value of murphys constant would be counterproductive, though it is a small affect. It may be a statistical fluctuation. Restricting to locations with a value < 3.5 would leave an average of 62.77

A value of pi below the normal value also looks harmful, though one that is too high also looks counterproductive. It looks like a relatively modest effect though and I don't wan to exclude too many possible locations, so I won't exclude any locations based on the value of pi.

There are few high performing ones between latitude -38 and +38.
There are few high performing ones around shortitude 0, and  +-90
There are few high performing ones around deltitude 0, and  +-90
But this might be caused by the small number of bases in these areas.

I then fitted a simple linear trigonometric model to the records that had the other properties that were identified with high performance. This gave the following model:

90.40498684665667+1.0177516945528096*sin(deltitude)+11.356095534597717*cos(deltitude)-0.17160136718146096*sin(shortitude)+14.734915658705445*cos(shortitude)-2.41427525418688*sin(latitude)-62.034325081735766*cos(latitude)+5.158741059290979*sin(longitude)+8.287780468342245*cos(longitude)
Standard deviation of error is 13.19479724158273 The no of records was 180

I found that the standard deviation error was reduced when degrees  were converted to radians using the local value of pi, so that is what was used.

This predicts that the following 12 possible locations have the best performance:

38730 VALUE:110.47214318466737
103420 VALUE:110.67976641439135
91328 VALUE:111.69109272372066
26403 VALUE:112.35848311090837
7724 VALUE:112.40205758474453
21409 VALUE:113.21091851443907
89352 VALUE:113.88444725998731
3090 VALUE:113.89351821821175
65317 VALUE:121.11038526877846
57364 VALUE:123.12690147352956
26627 VALUE:132.5469987591373
91627 VALUE:134.17450784571542

In practice I think it is unlikely that all of them will be greater than 100, but it looks like it will probably be good enough to please the empress.

 My best estimate is:

Hammer Hurler
Matchlock Marauder
Professor Pyro

This is also my entry for the PvP contest

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