Are you happy or unhappy? (You thought it was over?)
A slight change in the problem:
Remember, in the previous problem, we were taking one dot away from the first sector and putting it in the next sector. Then, we took away two dots from the second sector and put it in the next sector, and so on and so forth.
What happens if instead:
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Take one dot from first sector, put it in next sector.
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Take two dots from 2nd sector (from where you just put 1 dot in) and put it in next sector.
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NOW Instead of taking one away from the next sector, you take 3 dots away from the next sector.
And repeat the pattern.
Of course, the same rules apply for happy and unhappy number as from before.
What is the largest happy number with these new rules lower than 5,000,000,000?
For the original problem, go to the "My favorites" set and find the problem, Are you happy or unhappy? OR go to this link:
https://brilliant.org/profile/jonathan-ydncjm/sets/are-you-happy-or-unhappy/
Remember, follow for more cool stuff! (Is this the end of the happy problem?)
The answer is 3486784404.
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I think I notice something about these happy problems. I modeled them out with some blocks and was playing around. I noticed that the first block you move never goes away. This is obscure to the human eye at first, because dots are identical. Anyways, I took away the block, and I noticed that we can skip doing anything with every alternate section. Now if you play for a while, every section has two blocks. This was just a start to it all, but I stopped here, and noticed the form of happy numbers, and transferred that to the newest problem. **I am not going to say the complete solution because of other trolls from Lexington. If you want me to explain it fully, I will do so.