This is how it happened...
07:22 : Mavis sends the picture to me by chat client.
09:32 : I notice it coming back from the bathroom and decide to try.
10:06 : I got fed up and Google it.
10:07 : Send the solution to her, making her quite impressed :-)
So what was it that I got fed up of ? See picture:
The answer to the problem is: 2. Turns out that the right hand side number counts the number of circles appearing in the left hand side expression. Now, I have no problem with pre-school kids solving problems that I cannot solve, but the thing that bothers me is that the problem is very badly formulated to start with. The *should* have been formulated as follow
8809 = ****** 7111 = 2172 = 6666 = **** 1111 = 3213 = 7662 = ** 9313 = * 0000 = **** 2222 = 3333 = 5555 = 8193 = *** 8096 = ***** 7777 = 9999 = **** 7756 = * 6855 = *** 9881 = ***** 5531 = 2581 = ?
You see, the solution indicates that the left hand side was representation dependent while the right hand side wasn't. This should have been made clear in the formulation of the problem itself. And don't give me the "Yes, Pascal but that was the interest of the problem". No it wasn't. The reason why the pre-schooler do it is because the left hand side creates a buffer overflow in their minds, so they default to paying attention to the *representation* of the numbers, while the right hand side does not overflow and they focus on the *meaning* of the representation (leading some of them to realize that there might be a correspondence). On the over side, the mind of "higher educated people" not only works fine most of the time, but they have had time (during their education) to learn to distinguish between meaning and representation. So of course they are not mentally tempted to look for the solution where they know it cannot be found (since they mentally assume that whomever posed the problem is not stupid).
Additionally, you will notice that there is a very good reason for this problem to have been given as a picture, and not a text. That's because some fonts (such as the one I am looking at right now while typing this text on my computer), render the number "0" with a oblique bar changing the number of "circles" in it. Resorting to a picture (which was the only way to make the problem "font-independent") makes the very point I am making in this entry.
This matters to me because years later, when those pre-schoolers become adults, I have a very hard time explaining to them the following equality
(where the trailing dots have the obvious meaning of infinite expansion). This issue is so famous among teachers of first year maths students that it even have its own wikipedia page.
And what's the thing with "programmers". Does the problem's formulation somehow suggests that they are half way between "clueless" and "educated". How are higher educated programmers supposed to perform ?
Anyway. I am better than a pre-schooler, because now that I have actually *understood* the problem, I have a method to construct an endless number of "problems" that can only be solved by "pre-schoolers", as to impress my friends during parties (and call myself clever when they don't get it): mix representation and meaning.
And now that I have understood that, next time I cannot solve one of those pre-schooler problems, I will remember today's experience and look for the solution in representations, shapes, sounds, anything a kid might pay attention to given the low buffer capacity of their minds. If I do succeed, what does that make me ? The next stage after "higher educated" ? Is that "hyper educated" ?...