FAKE DIAMONDS
You can find the fake diamond in three weighings. Step by step:
Step 1
Divide the gems into three sets of eight. Weigh one set against the other on the scale. If it balances, then the unweighed set contains the fake. If it does not the lighter set contains the fake.
Step 2
Divide the set of eight containing the fake into three subsets of three, three and two gems. Weigh the two sets of three against one another. If one is lighter, it contains the fake. If they are equal, then the set of two contains the fake.
Step 3
If the fake is in the set of two, weigh these gems against one another. The lighter will be the fake. If the fake is in a set of three, take two of those gems and weigh them against one another. If one is lighter, it is the fake. If they are equal, then the one remaining gem is the fake diamond.
PRISONBREAK
You should ask one of the prisoners which door the other would tell you hides the prison guards. You escape through this door.
TICKS
One soldier has four ticks, the other has two.
MASONRY CLEANING
The church spire is 14 metres tall.