What rule do “2, 4, 8” follow?
Most riddles require you to solve a problem or find an answer given a certain number of variables. In this Veritasium video, Derek Muller goes around talking to people and proposing a riddle with a twist.
He gives passersby three numbers — 2, 4, 8 — and challenges them to come up with the rule he used to choose those numbers. To do so, they are allowed to propose any three numbers, and he will tell them whether they follow his rule.
Some guesses are “16, 32, 64,” “3, 6, 12,” and “5, 10, 20,” and although all of these sets follow his rule, he tells everyone that the rule is not that you need to double the number in each case.
You can see people getting more and more frustrated, until he begins to give clues.
Before you read any further, think about how you might approach this riddle. What three numbers would you ask about? If you want to try it out, you can do so here.
The first clue that he gives leads someone to guess “2, 4, 7.” Interestingly enough, that fits his rule. Soon, you can hear people guessing very different sets of numbers: “3, 6, 9,” “5, 10, 15,” “8, 16, 39,” etc. Nobody is any closer to guessing the rule because Muller says yes to all of them.
Chances are, whatever three numbers you picked follow his rule. It’s a pretty simple one: the three numbers must be in ascending order. Nobody thought to ask about something like “8, 4, 16.”
The moral here is that we tend to ask questions that confirm what we already believe. The more questions we ask that point to a theory, the more we’ll be sure that it is correct. However, it’s impossible to confirm a theory true, you can only disprove one with a counterexample.
As Muller mentioned, if you believed that all swans were white, and all you ever saw were white swans, you would become increasingly convinced. However, it would only take seeing a single black swan to change your mind.
The trick in this puzzle is to try to find numbers that will lead to a “no.” They will give you much more information than a “yes, they follow the rule.”
“That’s what is so important about the scientific method,” says Muller. “We set out to disprove our theories and it is when we can’t disprove them, that we say this must be getting at something really true about our reality.”
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