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.
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.