The first portion of darkness

We'll see how the Dragon can force you to make bad decisions. Let's introduce some darkness into our model. Please solve the third example:

$$729, 512, 343, 216, ? (3)$$ (5)

The answer is 125 as and the rule is:

$$X_{i} = ( 9 - i )^{3} %%(3a)$$ (6)

Maybe a programmer can quick remember that 512 is the cube of 8, but it is simple for you to see in 343 the cube of 7? You rare use this fact in your work and it is dark for you.

The third rule is as simple as the second. The exercise is more complex. To find the rule you need to find the order of facts. This facts are harder to find out.

We can see this on the next example. The rule is very simple, if you know it.

$$4, 9, 10, 19, 24, ? %%(4)$$ (7)

How many time do you need to find a solution?

Here is a swindle. The numbers are in the hexadecimal format. Let's rewrite the sequence in the more usual form:

$$4, 9, 16, 25, 36, ? %%(4a)$$ (8)

Now you can recognise the squares of 2, 3, 4, 5 and 6 much better. The answer is 31 what equals 49 in decimal format.

Suppose you don't know about the trick with the hexadecimal format. If you think this is a sequence of ordinary numbers, you may find some solution. Probably it won't be simple and your answer won't be 31.

The difference between hexadecimal and decimal numbers is the source of many misterious errors. I think each programmer had made them. Above all on the start of his career.

Let's consider the problem of the difference on other examples.