The first line looks like familiar mathematics but by the second it is clear that perhaps the cross symbol, traditionally associated with addition, is not being used in its conventional manner.
Browsing through some of the 2.1 million comments, there appear to be two frequently occuring responses, 40 and 96. The former arises as a result of imagining that the right-most column is a running total of those numbers on the left. This requires such an horrific misuse of the equals sign that I daren't contemplate it.
The solution which is easier to stomach is 96. Apparently, the addition sign is being used as a different binary operation on its adjacent digits. If we multiply the two numbers and add the first, we get the answer on the right. By this method we add eight to eight elevens and get the 'solution'.
The thing that really riles me with this post, however, is the statement above: "only one in a thousand will get it". This is not true for the simple reason that any answer is correct.
Let me explain.
Supposing the answer is indeed 96. This just means that there is one rule that outputs 5, 12, 21, and 96 when entering the pairs (1,4), (2,5), (3,6), and (8,11). If we call the first of this pair x and the second y then one way of combining them is to use the formula (with addition used in its conventional sense)
Suppose I wanted the golden question mark to represent 100. All I would need is a formula that keeps the first three answers correct and outputs 100 when x is 8 and y is 11.
Here's one:
OK, so it's a little more complicated-looking but it is not an approximation. The answers come out precisely. Try it yourself.
Interestingly, this formula isn't unique. There are plenty of others I could have calculated that give the required answers. There wasn't even any need to include y terms. A valid formula only dependent on x is even easier to find. This would feel like cheating though.
It is easy to see why this might work by imagining a picture. Suppose we have x and y axes lying flat and perpendicular on a table. Now imagine that when we pick a point on this plane, the outcome of the above formula is represented by a height. If we connect all these points, we get some sort of surface:
It will probably strike you that this is quite curvy. The ability for surfaces to flex like this helps us construct contrived solutions to the above problem. All we have to do, in order for 100 to be the 'answer' is to find one that passes through the four points in 3-dimensional space with coordinates (1,4,5), (2,5,12), (3,6,21), (8,11,100). There are, of course, infinitely many such surfaces.
You might be wondering how I stumbled across the formula above. It would have taken a very long time using trial and error but there's a very straightforward method. All that is required is to construct a separate term for each of the four pairs. The idea is that, for each pair you substitute in, three of the four terms disappear. The number zero is quite useful in this regard. If I wanted to make three terms disappear when I plugged in y=4, for example, then I could simply multiply each by a factor of (y-4).
In this way you can construct a formula that works for any chosen question mark. Here is an example:
You can see, in the last term, where to insert your favourite answer. Whatever you choose you will be correct; don't let the internet tell you otherwise.
from matheminutes http://ift.tt/1XQan5O
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