The question you opened
A brick and half a brick
A brick weighs 1 kilogram plus half a brick.
What does the whole brick weigh?
2 kg
Half the brick is the missing kilogram, so the other half is 1 kg too. Two halves of 1 kg give a 2 kg brick.
A brick weighs 1 kilogram plus half a brick. The brick weighs 2 kilograms. The sentence describes the brick in terms of itself, which is what makes it slippery. Call the brick b. The sentence says b equals 1 plus half of b. Take half of b off both sides and you get half of b equals 1, so b equals 2. There is a version you can do without algebra, and it is more satisfying. The brick is made of two halves.
The sentence says the whole brick equals 1 kilogram plus one of those halves. So the part left over after removing one half, which is the other half, must be the 1 kilogram. If half a brick is 1 kilogram, the whole brick is 2. The wrong answer of 1.5 comes from reading half a brick as half a kilogram. That reading is understandable, since the kilogram is the only weight mentioned, and the phrase half a brick has no number attached.
Substituting the known quantity for the unknown one is the actual error, and naming the unknown out loud is what prevents it. Self referential descriptions like this turn up more often than they should. A tip that is 20 percent of the total, where the total includes the tip. A tax on a price that includes the tax. A bonus that is a percentage of profit, where profit is measured after the bonus.
In each case the quantity appears on both sides, and treating it as known on one side produces a number that is close and wrong. The recipe is always the same. Give the unknown a letter, write the sentence as an equation exactly as it reads, then collect the unknown on one side. Two lines of work, no cleverness required. The classic version of this puzzle uses a bottle and a cork, or a bat and a ball. Same structure, same reflex, same fix.
Technique: Name the unknown, then read again