Week 2 - Solution: A Long Combination

How did you like this new kind of puzzle? Did you figure out what the Long Combination is? Which 24 numbers open the lock on the Silverquicken Armory door? If you're still working on it, STOP HERE! Spoiler Alert: We WILL discuss the solution to the puzzle in this post, so if you don't want to see it now, come back later!

You probably noticed that the numbers go up and down according to two different patterns: ODD numbers go UP (and by how much? You multiply by 3 then add 1), and EVEN numbers go DOWN (you divide by 2). These rules create a long string of numbers that are nicknamed “hailstone” numbers, because they go up and down like hailstones in a cloud. Here's a picture of the final solution. Are these the 24 numbers you came up with too?

 

And here you can see "BJK GOAT" again, solving this week's puzzle and explaining how he thought through it.

For a challenge, try starting with 27 instead of 25. It will take you over 100 steps to get down to 1 -- and you’ll go higher than 9,000 along the way! Have a calculator handy for this one. Starting at 31 is also a doozy.

In 1937, a mathematician named Lothar Collatz asked whether these numbers would always drop to 1, no matter what positive whole number you started with. Could you just bounce around in the “number clouds” forever without falling to earth? To this day, no one knows the answer! 

(This is the kind of thing that professional mathematicians work on. They try to answer math questions no one knows the answer to.)

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