> They're not tests of intelligence so much as tests of how similar your pattern matching is to that of the test authors.

Well... they are tests of intelligence. A valid test of intelligence is one that lets you determine ("predict") the intelligence of a testee from their answers. For that, you need intelligent and unintelligent people to have measurably different answer patterns, but there is no requirement that the intelligent answer patterns be objectively correct. You could have a test that was entirely subjective ("Who was the better artist, Michelangelo or Jackson Pollock?") and still use it to predict intelligence[1].

[1] That's an invented example; I'm not claiming that the particular question of Michelangelo vs. Jackson Pollock is actually predictive of intelligence, just pointing out that it could be.

But how do you select 'intelligent' people to generate your 'intelligent' answers? If it's not at some point tied back to some kind of objective performance (generating correct answers) then you're not measuring intelligence.

That's wrong. If your subjective test agrees in result with your objective test, they're measuring the same thing. That we can't begin the study of intelligence tests with a fully subjective test wouldn't mean we can't end there (and in fact, we can begin that way, because we start off with the idea that someone is smart if other people are inclined to describe them that way, not that someone is smart if they do well on a math test).

These are not intelligence tests, they're cognition tests. The goal is not to seek the correct answer, but a correct answer.

Seeking a correct answer is trivially easy, though; you can always find the rule "any of the six shapes on the left", just as you can always fit a function to any arbitrary sequence.

Right, but the context is that these problems comprise an evaluation suite for artificial intelligences. Even simply textually describing the shapes on the left and the right, is an accomplishment.

A better test suite would likely provide an oracle capable of generating new images belonging to the left or right and asking the program to judge which side it belongs to.