Now they should be thinking of Denmark and you request an animal that begins with the last letter from that country's name. This will normally be a kangaroo and from there you ask for a colour beginning with the final letter of that word. Noy you can proclaim, "Ah come on! There are no orange kangaroos in Denmark".
Going four->Denmark->kangaroo->orange is simple enough, but how do we make sure that every time out we turn there number into four? You have done it hundreds of times before.
The answer of course is algebra. You let your number equal x and then manipulate it to 4. For example,
- add 4 => x + 4
- multiply by 2 => 2x + 8
- add 4 => 2x + 12
- add your original number => 3x + 12
- divide by 3 => x + 4
- subtract your original number => 4
All very easy but I was very impressed when I learned this method. I was doing a variation where you keep going for about 10 steps, get them to close their eyes, and ask them if they feel silly (or some such). I was seated with the Scottish team at a bridge event and asked my right-hand companion to pick a number. I heard him murmur 'x' under his breath, and I just said, "wow, that is really clever." I think it is one tool every secondary school student should have in their cognitive toolkit.