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Hmm, yeah it's a bit hard to try stuff when there's no good preview. Usually I'd recommend rot13 chiffer if all else fails but for number sequences that makes less sense.

Some 2-4-6 problems

by abstractapplic

1 min read28th Mar 20239 comments

28

Exercises / Problem-SetsRationality

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This is a linkpost for https://h-b-p.github.io/twofoursix/

The sequence [2, 4, 6] is valid. Test other sequences to discover what makes a sequence valid. When you think you know, write down your guess, reveal the rule, and see how it compares.

(You should try to deduce the truth using as few tests as possible; however, your main priority is getting the rule right.)

You can play my implementation of the 2-4-6 problem here (should only take a few minutes). For those of you who already know the solution but still want to test your inductive reasoning skills, I've made some more problems which work the same way but apply different rules.

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[-]Viktor Rehnberg4mo70

I knew about 2-4-6 problem from HPMOR, I really like the opportunity to try it out myself. These are my results on the four other problems:

indexA

Number of guesses:

8 guesses of which 3 were valid and 5 non-valid

Guess:

"A sequence of integers whose sum is non-negative"

Result: Failure

indexB

Number of guesses:

39 of which 23 were valid 16 non-valid

Guess:

"Three ordered real numbers where the absolute difference between neighbouring numbers is decreasing."

Result: Success

indexC

Number of guesses:

21 of which 15 were valid and 6 non-valid

Guess:

"Any three real numbers whose sum is less than 50."

Result: Success

indexD

Number of guesses:

16 of which 8 were valid and 8 non-valid

Guess:

"First number is a real number and the other two are integers divisible by 5"

Result: Failure

Performance analysis

I'd say that the main failure modes were that I didn't do enough tests and I was a very bad number generator. For example, in indexD

I made 9 tests to test my final hypothesis 4 of which were valid, that my guess and the actual rule would give the same result for these 9 tests if I were actually good at randomizing is very small.

I could also say that I was a bit naive on the first test and that I'd grown overconfident after two successive successes for the final test.

[-]Caridorc Tergilti4mo60

Here is my playthrough with my though process:

:::spoiler

>!0) [2, 4, 6] is VALID

>!Now I think, let's check if the rule is *2
>!1) [31, 62, 93] is VALID

>!Let's check if the rule is always true with 3 random numbers.
>!2) [6534525, 142536, 456342532] is NOT VALID

>!I wanted to check multiply by 3, but I repeated multiply by 2
>!3) [5, 10, 15] is VALID

>!Checking multiply by 3
>!4) [7, 21, 63] is VALID

>!Checking multiply by 10
>!5) [50, 500, 5000] is VALID

>!Now I am thinking: maybe any multiplication is ok? I cannot try them all, let's try constant addition:
>!6) [34, 35, 36] is VALID

>!Let's try constant subtraction
>!7) [5, 4, 3] is NOT VALID

>!Let's try increasing
>!8) [5, 64, 234] is VALID

>!Let's try increasing with random numbers
>!9) [12345, 123456, 1234567] is VALID

>!Let's try increasing or constant.
>!10) [5, 5, 6] is NOT VALID

>!Now I have made up my mind!

>!After 10 tests, your guess was . . .

>!"The sequence is valid if it is strictly increasing."

:::

[-]Viktor Rehnberg4mo10

See FAQ for spoiler tags, it seems mods haven't seen your request. https://www.lesswrong.com/faq#How_do_I_insert_spoiler_protections_

[-]Caridorc Tergilti3mo10

I tried both and neither works

[-]Viktor Rehnberg3mo10

Hmm, yeah it's a bit hard to try stuff when there's no good preview. Usually I'd recommend rot13 chiffer if all else fails but for number sequences that makes less sense.

[-]tay4mo63

Hey, it seems the app is getting its own rule wrong. :)

It says "Three numbers in ascending order"; however [0;0;0] is accepted as valid. It should say "in non-descending order".

[ADDED] Also indexA

shows the rule "Two odd numbers, one even; any order" but does not accept [-1, -2, -3].

[-]abstractapplic4mo30

Well, that's embarrassing. Fixed now; thank you.

[-]Measure4mo40

I got 1 right, 1 partially right, and 2 I couldn't figure out and gave up.

[-]Charlie Steiner4mo40

Have you played the game Understand?

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