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.
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.