# Are we scoring numbers now?

So from a couple other puzzles, you might remember that I'm a professor of Awesomeness at the Ad Hoc University! This time, I've given my students some numbers and their scorez. They need to tell me how I scored them!

Here we are:

197 = 26 + 592 = 618

1 = 0 + 1 = 1

1337 = 44 + 8584 = 8628

43770 = 163 + 83104 = 83267

7 = 16 + 52 = 68

2020 = 63 + 2752 = 2815

Hint 1:

You remember how I said "Note: all the information of the puzzle is in the blockquote; nothing outside the blockquote is relevant!" in my Scoring a grid puzzle? Yeah, well I didn't say that here!

First off

The 'strange' letters in the introduction are:
A oc t z ll
These are either written in italics or in z's case slang in 'scorez'

aoctzll is an anagram for collatz (and also lolcatz)

This of course hints towards

The collatz conjecture, a famous unsolved problem in mathematics. Simply put, do the following to a positive integer until it's equal to 1
- If it's even, divide by 2
- If it's odd, multiply by 3 and add 1

Now let's note:

If we take the leftmost number $$n$$ of each line, apply the collatz procedure to it, count the number of steps $$s$$ it takes to reach 1: The next number in the line is always equal to $$s$$.
And the next, third, number is the highest value the procedure reaches in between. Adding those two together is the final score.

• Hmmm, not sure why this was downvoted. Nice spot Lukas +1 – Stiv Sep 28 '20 at 15:02
• Great job! You just beat out David G. – Voldemort's Wrath Sep 28 '20 at 15:14
• Also, nice find with the lolcatz thing. That's hilarious. – Voldemort's Wrath Sep 28 '20 at 15:17

Starting with the answer by @Lukas Rotter:

I had notice A oc t ll
but I missed the z. I think my brain just elides spelling errors in public forums.

And @Lukas Rotter is correct, it is based on the Collatz conjecture.

I looked at it more deeply, and found, that in A = B + C = D

A is the starting number.
B is the number of iterations to reach 1.
C is the highest number reached.
D is B + C

Thus, for example, we would see:

3 = 7 + 16 = 23

Because the sequence is:
3, 10, 5, 16, 8, 4, 2, 1
7 steps, max of 16

• Nice job! Unfortunately, Lukas edited his answer 2 minutes before you posted yours, so he is correct. – Voldemort's Wrath Sep 28 '20 at 15:14
• I hate it when it takes too long to write my answer. – David G. Sep 28 '20 at 15:16

I am going to give it a try, hoping that my answers are correct..

$$197=9+9+7+1=26$$
$$97*(7-1)+9+1=592$$
$$26+592=618$$

$$1=1*0=0$$
$$1^1=1$$
$$0+1=1$$

$$1337= (7^2+1)-(3+3)=44$$
$$(7-1)*1337+337+133+(33*3-7)=8584$$
$$44+8584=8628$$

$$43770=(7*7*3)+(7+7+3)-3^0=163$$
$$3*377*70+(4377-437)-(7+3-4)=83104$$
$$163+83104=83267$$

$$2020=20+20+20+2^0+(2+0)=63$$
$$(20*20*7)-(20+20+7+2^0)=2752$$
$$63+2752=2815$$

• Can you explain why you think this is the answer to the puzzle? I'm not sure I see any logic here - it looks like randomly arranging digits and operations, with no particular pattern. – Deusovi Sep 27 '20 at 21:20
• Very interesting try! (+1) It's rather convoluted, though, and not correct. – Voldemort's Wrath Sep 27 '20 at 21:20
• The logic is using the digits of the numbers in the first column of the question to formulate the numbers beside them.. In my opinion there is no pattern in the numbers given in the question. – Vassilis Parassidis Sep 27 '20 at 22:42
• @Voldemort's Wrath. By putting 1, I mean (+1). – Vassilis Parassidis Sep 27 '20 at 22:43
• What do you mean by comment #2? And if you don't see a pattern, then you're mistaken, not the question. – Voldemort's Wrath Sep 27 '20 at 23:49