@Juber - please read!
There are so many suggestions and solutions to get the golden box without spending money and diamonds - but no one has yet found a solution that works for people who have a life outside of FOE and a job every day from 07:00 - 17:00.
Please confirm that the above has been passed on to the developers and please come up with an explanation on how to get the building to lvl 10 without using diamonds/money when you have a job and a life outside of FOE.
Level 10 with time constraints (still assumes you can get on at 2-3 different times a day) and no diamonds:
Aim for as many cities as you *can* do (at least 10 cities is ideal including the short one at the start so that you hit 300 tasks = 1 guaranteed set of 5 golden fragments) = 1 every 2 days (and a bit) which should be comfortable enough to do if you have "some" time and follow the same strategy as people trying to squeeze in 1 every day practically but with more off-time - it's still important to minimize managers to some extent (not quite so extreme because less cities), because you need enough pots of gold to buy full sets of chests 2-3 times. But the more cities the better the odds.
You should always include festival manager 3 & shipyard manager 3 in every run for time constraint reasons; level 4 on one, the other, or both can speed up a run, but adds a lot of extra cost to it - so should be minimized.
Other managers are primarily for tasks and automation, and should be minimized with some tasks that require expensive managers skipped. You can take level 1 in each manager at least for automation purposes.
You'll find people's "speed run" strategies lists exactly which members to skip (you may not be going as fast as them, but they've done the math on which tasks are the most wasteful - you want to hit 32+ tasks per city to validate that the speed run in question is going to be suitable for your purpose).
Don't be unlucky and see fragments at least twice (or three times if 10 cities turned out to be too many) ; buy the chests when fragments show - if you get them 3 times you can adjust towards running less cities. (No way to avoid this if under both time constraints and no-spending constraints)
Your odds (assuming 1/3 chance of seeing fragments) can be pulled from this table - 10 cities needing 2 or more sets of fragments is just under 90%:
Towns Completed | 1 or More | 2 or More | 3 or More |
1 | 33.33% | 0.00% | 0.00% |
2 | 55.56% | 11.11% | 0.00% |
3 | 70.37% | 25.93% | 3.70% |
4 | 80.25% | 40.74% | 11.11% |
5 | 86.83% | 53.91% | 20.99% |
6 | 91.22% | 64.88% | 31.96% |
7 | 94.15% | 73.66% | 42.94% |
8 | 96.10% | 80.49% | 53.18% |
9 | 97.40% | 85.69% | 62.28% |
10 | 98.27% | 89.60% | 70.09% |
11 | 98.84% | 92.49% | 76.59% |
12 | 99.23% | 94.60% | 81.89% |
13 | 99.49% | 96.15% | 86.13% |
14 | 99.66% | 97.26% | 89.47% |
15 | 99.77% | 98.06% | 92.06% |
16 | 99.85% | 98.63% | 94.06% |
17 | 99.90% | 99.04% | 95.58% |
18 | 99.93% | 99.32% | 96.74% |
19 | 99.95% | 99.53% | 97.60% |