Yeah so this is a really
interesting puzzle because it turns out the puzzle itself is wrong. So not only do you have to solve the puzzle you have to figure out what the puzzle really is. It combines two of my interests: error correction and sequences. So I found this sequence on a website, actually a Dutch website, although that's irrelevant. It's a sequence that came up as part of a quiz. The quiz begins by asking you to identify various things, looks like
some kind of a thing- (Brady: I know that word!
I know that word; voorwerp, that means object.
- Aha! The third page has a number sequence
on it and they ask you what's the number that goes where the question mark is? And the sequence goes 1, 2, 6, 21, 85, question mark, followed by 2586. Now you stare at this and you cannot figure it out; I didn't see any pattern. So at the end you can look up the answer and the answer they give is 430. (So you had to cheat to look up the answer?)
- I cheated to look up the answer, because I couldn't figure it out! And since I am supposed to be an expert in sequences I wanted to know, what is the sequence that I couldn't figure out? And once I knew what they thought the answer was I could figure it out. And so what they did had a mistake in it. How do you go from 6 to 21? You add 1 and multiply by 3 and we get 21. So how do you go from 2 to 6? You add 1 and you multiply by 2; add 1 you get 3 times 2 is 6. How do you go from 1 to 2? You add 1 and multiply by 1; 1 plus 1 is 2 times 1 and you get 2. Okay, so so you stare at this and you say 'how do you go from 21 to 85?' Well if you add 1 and multiply by 4 you do not get 85, you get 88. The person making up the test did it in the wrong order. They multiplied by 4, to get 84, and they added 1 and they got 85. How did they go from 85 to 430? They added 1 to get 86 and multiplied by 5 and got 430.
- (So they started doing it) (right again?)
- They started doing it right again, so that's the answer.
- (How long did it) (take you to figure out what the mistake) (they'd made was?) Well the pattern- once you look at how you might go - this is something you always do when you're looking at a sequence and there's no obvious mathematical rule - you say to yourself, how can I go from 2 to 6? How do I go from 6 to 21? You try to think of a way to build it up and, well, there's a this part is one of many possibilities but it works and so, well, all right then it became clear that there was a mistake. [Preview] It's one of the
most basic things that we can do. And even now, even when we have digital images from great big telescopes, we still get a lot of information by looking at them with our eye.
