goes so far as the number is concerned, anyway, in which the clue is encountering a "take away the number you first thought of" after a trivial bit of maths that doesn't change the magnitutude of your initial random element.
If you're bothered enough to follow the process step by step, see the following.
Think of a single-digit number (though it's not necessary to be single-digit, to be honest)
0, 1, 2, 3, 4, 5, 6, 7, 8 or 9 (hereafter known as 'n')
Double it
0, 2, 4, 6, 8, 10, 12, 14, 16 or 18 ('2n')
Add 8 to the result
8, 10, 12, 14, 16, 18, 20, 22, 24 or 26 ('2n+8')
Divide the result by 2
4, 5, 6, 7, 8, 9, 10, 11, 12 or 13 ('(2n+8)/2)', i.e. 'n+4')
Subract the original number you thought of (This is the giveaway bit)
4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ('n+4-n', i.e. '4', always)
Convert that number to a letter. (1=A, 2=B, etc)
This will be 'D'.
Think of a country that starts with that letter
This is the psychological part. Most people will think of Denmark as a country beginning with D. Occasionally someone will choose something else. Probably to be perverse, or because they are familiar with Djibouti (Republic of) or Dominica (Comonwealth or Republican).
Think of an animal whose name starts with the second letter of that country
If Denmark, then 'E' is the starter... Well, Elephant is another logical choice. (Although other options exist, e.g. emus, elks, or eurasian pygmy shrews, on the whole your average person won't choose any of them if not trying to defeat your 'trick'.)
Think of the color of that animal
Apart from Pink, or possibly White, really it's quite obvious what colour to think of. And if you're still under the impression that your initial choice of digit is still chaotically skewing the output you're probably not too bothered about that.
Lern2Geography, there are no gray elephants in Denmark, fool
Of course, we all now know that it's a largely convergent process. Unless you've done the sums wrong or deliberately chosen an Orange Dominican Orangutan.
For some mathematical twists (multiply by nine, add the resulting digits together) it needs to be 1..9 to converge on a single answer straight off, but you can deal with higher 'random' numbers in other ways. Or even revel in them (adding a five digit number to a reversed-digit version of itself, along with some other mathematical wizardry to ensure eventual convergence on a predictable solution, looks particularly astounding if used well).
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