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I bring my summary to your attention. Mind, please, that there are people who burnt a fortune but completed all 3 tasks. So technically the event is solvable. I aim at reasonable expense of resources. A boost run, mentioned below, means all drop rate improving power-ups active - SC+GD+D+SG. To finish Task 1 and 2, IMHO, we need only 2 boost runs. What to do with the 3rd - I can't say. Maybe drop rate will improve closer to the deadline.

Age of Ashes is a unique event with shifting parameters and even changing terrain.

1 period, 20-17 days: no penalties

2 period, 16-?? days: +10% fuel to Volcanic flights

Task 1. My estimate is: 400-500 Chainsaws and 2 boost runs needed.

3 Gates of Hell collections needed to finish the event

Its items drop from Burnt Trees around your city

Chainsaws are needed for that

Chainsaw is an event item and we exchange it vastly

Chainsaws drop from neighbors' Burnt Trees

chance: 20%, +SG 40%, +all bonuses - up to 80%

Particulate Filter drops from your Burnt Trees

chance: 20%, +all bonuses up to 60%

8 event routes give Volcanologist Equipment collection

Every flight needs Particulate Filter - drop rate up to 80% with all bonuses

Every collection gives Institute of Volcanology (36 coins / 20 min)

The goal is to get all 6 in one boost run

24 new stars are strictly limited by the number of Filters

Task 2. My estimate is: 60 Filters and one boost run needed, then clicking

3 They're not Rocks, They're Minerals collections needed to finish the quest

Its items drop from Volcanos at your city once an hour:

chance: 10%, +all bonuses - up to 80%

Jackhammers are needed for that

They are produced by Institute of Volcanology every 20 min:

chance: 20%, +all bonuses - up to 100%

Task 3. My estimate is: it can be finished only with terrible expense of resources

3 Cold War collections needed to finish the quest

Items drop from 8 common flights - chance: lower than 1/100 

Bali (T-P) needs Landing Lamp

Los Angeles (J) - free!

Lima (D) - free!

Iceland (P-D) needs FC

Seattle (Jum) needs FH+FC

Bogota (G) needs FC+Bl

Anchorage (F) needs FL+EP

Osaka (T-B) needs Bed+ER ?

10 give Jumbo Ranger - a modified Jumbo +20% speed!

The final prize is The Capitol. It produces 1 item a day.

Small side quests:

1. Mountain View.  Visit 3 Research Labs of your neighbors.
   
2. First Victims.  Tap 5 Burnt Trees at your neighbors' cities.
   
3. Ashes to Ashes. Find 1 Chainsaw.
   
4. Deeper investigation. Cut 5 Burnt Trees with Chainsaws.
   
5. Household Objects. Find 1 Particulate Filter.
6. Keeping a Distance. Take a flight to Mount Elbrus.
7. Philanthropists in the Woods. Find a Rock Hammer in your Burnt Trees.
8. Thermal Imager in Hand. Assemble the Gates of Hell collection.
9. Full-on Panic. Visit 25 residential buildings.
10. Through the Smoke and Lava.  Assemble 1 Volcanologist Equipment collection.
11. The Scientific Method. Build 1 Institute of Volcanology.
12. Grim Prospects. Visit Institute of Volcanology 10 times.
13. The Radioactive Smithereens. Visit Institute of Volcanology 1 time.
14. The Root of the Matter. Find 1 Jackhammer.
    
15. Community Service. Assemble the They're Not Rocks collection by studying the Volcano.
16. Sweaty Work. Visit Institute of Volcanology 5 times.
17. The Inevitable Explosion. Visit 25 residential buildings.
18. A Cold Decision. Bring a Nitrogen Cylinder from LA.
19. The End is Near. Visit 10 Coffee Bars.
20. Untapped Potential. Visit 10 Eateries.
21. A Dark Cloud. Visit 5 Flower Shops.
22. Giant Mushroom. Visit Car Dealership 3 times.
23. History in the Making. Visit 20 Cottages.
24. A Sober Reckoning. Complete the Cold War collection.