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Each truth-teller answers yes to just one question; each liar answers yes to three of the questions. Therefore, we can figure out the correct answer by considering the number of yes answers:

Y = total "yes" answers (150)
L = number of liars
T = number of truth-tellers
I = number of islanders (100)

I = L + T
L = I - T
L = 100 - T

Y = 3L + T
150 = 3*(100 - T) + T
150 = 300 - 3T + T
150 = 300 - 2T
2T = 150
T = 75

T = 75
L = 25

You get it by wearing the following equipment with the following constant effect enchantments:
Armour:
Daedric Face Of God - Fortify Heavy Armor 1 - 29 points (re-equip until you get 29)
Daedric Left Pauldron - Fortify Heavy Armor 1 - 1 point
Daedric Right Pauldron - Fortify Heavy Armor 1 - 1 point
Daedric Cuirass - Fortify Heavy Armor 1 - 23 points (re-equip until you get 23)
Daedric Left Gauntlet - Fortify Heavy Armor 1 - 23 points (re-equip until you get 23)
Daedric Right Gauntlet - Fortify Heavy Armor 1 - 23 points (re-equip until you get 23)
Daedric Greaves - Fortify Heavy Armor 1 - 2 points (re-equip until you get 2)
Daedric Boots - Fortify Heavy Armor 1 - 9 points (re-equip until you get 9)
Daedric Tower Shield - Fortify Heavy Armor 1 - 89 points (re-equip until you get 89)
Clothing:
Exquisite Amulet - Fortify Heavy Armor 1 - 47 points (re-equip until you get 47)
Exquisite Ring - Fortify Heavy Armor 1 - 47 points (re-equip until you get 47)
Exquisite Ring - Fortify Heavy Armor 1 - 47 points (re-equip until you get 47)
Exquisite Robe - Fortify Heavy Armor 1 - 15 points (re-equip until you get 15)
Exquisite Belt - Fortify Heavy Armor 1 - 15 points (re-equip until you get 15)
Exquisite Shirt - Fortify Heavy Armor 1 - 23 points (re-equip until you get 23)
Exquisite Skirt - Fortify Heavy Armor 1 - 23 points (re-equip until you get 23)
Exquisite Pants - Fortify Heavy Armor 1 - 23 points (re-equip until you get 23)
Weapon:
Ebony Staff - Fortify Heavy Armor 1 - 35 points (re-equip until you get 35)

All those enchantments combine to give your Heavy Armor skill a boost of 475 points. You can push your base skill to 105 by completing a certain Tribunal quest, bringing the grand total to 580. The full set of Daedric armor gives you an armor rating of 1546.

I tested this in game, so I can confirm that it's correct.

If you consider the re-equip trick an exploit, then the maximum is 936.

The entire population of the town of Totleigh-in-the-Wold consists of the constables, crooks and commoners. Constables always lie to commoners, crooks always lie to constables, and commoners always lie to crooks. In all other cases, the townsfolk tell the truth.
One day a number of townsfolk were dancing in a circle round May Pole, and each one said to his or her right-hand neighbour, 'I'm a constable'.
How many commoners were dancing round the May Pole?

There are no Commoners.
If you start your circle with a Commoner, he is able to lie to a crook and say he is a constable, and the chain can continue on, with crooks and constables safely saying they are constables to other crooks or constables. However, when someone has to talk to the commoner, a crook cannot lie to a commoner, so he would have to say he is a crook and that's not possible as per the puzzle. If it is a constable talking to the commoner, he would have to lie, therefore he couldn't say he is a constable.

Basically, the only person who would be able to tell the commoner they are a constable is a constable, and because constables always lie to commoners, there is no way they could say that.

On the Moon, all objects weigh six times less than on the Earth, since the Moon’s gravity is six times weaker.
Now, imagine that there is a lake on the Moon. A steamship, which sinks five and a half metres deep into fresh-water lakes on the Earth, is lowered into this lake. How deep will it sink into the waters of this imaginary lunar lake?
An additional question: where does a person who cannot swim have a greater chance to drown: in a lake on the Earth or in our imaginary lunar lake?

Without thinking about it too much (cue careless mistake), it sounds like such things would be equal, since mass is equal on the moon, even if weight is not.

25 ?

22?

34?

29?

П ≈ 3,141592.......

We get each subsequent number by adding a digit from the П number to the preceding one:

1 + 3 = 4
4 + 1 = 5
5 + 4 = 9
9 + 1 = 10
10 + 5 = 15
15 + 9 = 24

The next digit in the П number is 2, thus, the answer is 26 (24 + 2 = 26).

A freight train is moving along a one-track railway. An express passenger train is approaching it from behind, and the freight train should let it pass.
How may it be done, if there is just one free feeder nearby, which has a dead end and is too short to fully contain either the freight or the passenger train?

Let's assume that the freight train is much longer than the passenger train (as they usually are), and that the feeder can contain half of the passenger train's carriages at once.

The freight train must pass the feeder, allowing the passenger train to put half of its carriages into the feeder. The freight train would then reverse backwards, allowing the half of the passenger train that was in the feeder to leave the feeder, and pass in front of the freight train. The process should be repeated for the remaining carriages.