People familiar with unit testing and test driven development will feel at home with this kind of puzzle. That doesn't mean that they will be less biased in social/political decisions, it just means that this test will fail to prove a point.
Seriously, though, it seems a bit of leap from the existence of confirmation bias to explaining away the public outpourings of US Politicians about their financial crises and foreign policy disasters - in the absence of better data as to just why the given statements were made ascribing this to confirmation bias seems itself open to accusations of confirmation bias! :)
This doesn't mean I always use these—at the very least, I have to explicitly jump into "problem solving" mode—but it means they can be useful.
It's still a meaningful difference, and could very well apply to lots of things beyond this kind of puzzle.
[3 5 7]
[7 5 3]
[8 4 2]
[5 7 3]
[1 2 3]
[1 1 1]
[0 1 2]
At that point, I correctly answered the question.
But it accepts zero percent of real numbers.
To talk about a certain fraction of real numbers you have to have a distribution over them. In general we take the uniform distribution if no distribution is explicitly given. That doesn't work for real numbers (it doesn't even work for natural numbers). (See https://math.stackexchange.com/questions/14777/why-isnt-ther...)
If there's no implicit default distribution, we have to pick on. I can pick one where they cover an arbitrary high percentage of real numbers..
We can't reasonably talk about a percent coverage, since the Lebesgue measure of the reals is infinite, but as a non-technical description, 'zero percent' is morally equivalent to saying it only covers a measure-zero set.
Most importantly I used about 6 tests (3 right 3 wrong) to come up with the answer and then did another 17 looking for the trick. After all, it couldn't just be that simple right?
So after the tests listed above I felt confident enough to guess.
I was relieved, in fact, when it worked with negatives and floats in a "safe" range.
I also tested with 1,1,2 and 1,2,2 to make sure that the required increase applied to ALL of the values, not just a specific pair.
The observation to brainstorm for ways of proving that a statement is in fact wrong, and exhausting them, is such an eloquent way of wording the hunt for a negative.
Like others here have said it wasn't a particularly hard "rule" to figure out. Easy to immediately rule out geometric relationship as in 2^y, which didn't leave a whole lot of possibilities to test. For the commenters here, I'd attribute ease of finding the solution to familiarity with the kinds of problems that programming presents.
Which leads to the idea there's value in learning even the rudiments of programming. Logically, it should encourage better problem-solving skills in general. We might think there this has important implications for our educational systems. But I know, that's probably not realistic at all.
4,6,8 Y 1,1,1 N 1,2,3 Y 1,6666,8777 Y 1,0,1 N 3,2,1 N 3,2,3 N 5,6,4 N 7,5,6 N
But I totally see why it would cause you to pause and rethink your original idea :).