[Daily puzzle] Fill in the blanks \ stacker news ~science

2347 sats \ 20 comments \ @south_korea_ln 29 Oct science

Fill in the blanks with a single digit such that the resulting sentence is true.

"In this sentence, the number of occurences of the digit 0 is ______, of the digit 1 is ______, of the digit 2 is ______, of the digit 3 is ______, of even numbers is ______, of odd numbers is ______, and of prime numbers is ______."

Previous iteration: #743084 (answer in #743754). Also, @Scroogey ended up solving the puzzle from 2 days ago: #741908

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500 sats \ 8 replies \ @Scroogey 29 Oct

Brute force finds two solutions:

1 2 3 2 5 6 7 1 2 3 2 6 5 6

1 sat \ 6 replies \ @0xbitcoiner 29 Oct

I think it's an impossible problem to solve!

12 sats \ 0 replies \ @south_korea_ln OP 29 Oct

This would be an impossible variant to this self-referential problem:

"In this sentence, the number of occurences of the digit 0 is ______, of the digit 1 is ______, of the digit 2 is ______, of even numbers is ______, of odd numbers is ______, and of prime numbers is ______."

(notice the omission of the digit 3 part)

0 sats \ 4 replies \ @Scroogey 29 Oct

What's wrong with either of my solutions?

1 sat \ 3 replies \ @0xbitcoiner 29 Oct

In this sentence, the number of occurences of the digit 0 is 1, of the digit 1 is 2, of the digit 2 is 3, of the digit 3 is 2, of even numbers is 5, <---- of odd numbers is 6, and of prime numbers is 7.

In this sentence, the number of occurences of the digit 0 is 1, of the digit 1 is 2, of the digit 2 is 3, of the digit 3 is 2, of even numbers is 6, <---- of odd numbers is 5, and of prime numbers is 6.

I'm considering that 0 is neither even nor odd

33 sats \ 2 replies \ @Scroogey 29 Oct

I think zero is generally considered even as it can be divided by two without remainder.

1 sat \ 1 reply \ @0xbitcoiner 29 Oct

Since the number zero is even, both are correct!

22 sats \ 0 replies \ @south_korea_ln OP 29 Oct

Yes, there should be two valid solutions.

I'll post the reasoned solution to this problem at the same I post the next problem tomorrow.

I like brute force solving problems in my daytime job. It's sometimes so much faster.

0 sats \ 0 replies \ @Scroogey 29 Oct

Code here

1 sat \ 0 replies \ @south_korea_ln OP 30 Oct

Reasoned solution:

Let the blanks be filled in with

, and

, respectively. Among these, the first four entries satisfy

for

, while the other three entries each satisfy

. Thus,

, and

. Given

, the values have opposite parity, so there’s at least one additional even and odd entry. Consequently,

and

. This limits

to only five pairs:

. Each pair has exactly one prime number, hence

, but

, as this “3” would add a fourth prime to the set, implying

Now, only

and

are potential placements for “1,” so

. If

, there are three primes, including one from

, but not

. Setting

would then leave only three primes, and any other

would be too large. Thus,

. Assume

; then

. To assess feasibility, suppose

, which implies

, creating a contradiction with

. Thus,

. If

leads to more than three primes, so

With

, counting primes from

yields five primes. Setting

results in six primes, while

yields five primes, a contradiction. Therefore,

, implying

because

would introduce three “2”s. Since only

allows a third 2, we conclude

and

Thus, we find six primes with

, resulting in two possible solutions:

and

0 sats \ 2 replies \ @SimpleStacker 29 Oct

This is the answer ChatGPT gave.

"In this sentence, the number of occurrences of the digit 0 is 2, of the digit 1 is 1, of the digit 2 is 2, of the digit 3 is 1, of even numbers is 3, of odd numbers is 3, and of prime numbers is 3."

0 sats \ 1 reply \ @south_korea_ln OP 29 Oct

Yeah, it's bad at this.

For other daily puzzles, i checked, it did arrive to the solution. But I'll just keep assuming people do it for the fun of solving rather than the few sats i give as rewards here and there. No way to police this anyhow :)

0 sats \ 0 replies \ @SimpleStacker 29 Oct

I wonder why they haven't built in the capability for ChatGPT to simply say, "I don't know." The solution it gave is so obviously wrong.

(I haven't used it for previous problems, not that anyone accused me. But this one seemed especially suitable to test on chatgpt, and it failed pretty miserably.)

0 sats \ 0 replies \ @Roll 29 Oct

“In this sentence, the number of occurrences of the digit 0 is 1, of the digit 1 is 11, of the digit 2 is 2, of the digit 3 is 1, of even numbers is 2__, of odd numbers is 1, and of prime numbers is __2."

0 sats \ 0 replies \ @UsgBtc21 29 Oct

For the digit 0: Note the number of occurrences of "0" in the sentence after filling in the blanks. Example: # There are X occurrences of the digit 0.
For the digit 1: Count the occurrences of "1" after filling in the blanks. Example: # There are X occurrences of the digit 1.
For the digit 2: Count the occurrences of "2" after filling in the blanks. Example: # There are X occurrences of the digit 2.
For the digit 3: Count the occurrences of "3" after filling in the blanks. Example: # There are X occurrences of the digit 3.
For even digits: Count all even digits in the final sentence and confirm their total. Example: # There are X even digits.
For odd digits: Count all odd digits in the sentence and verify their total. Example: # There are X odd digits.
For prime numbers: Count the prime digits (2, 3, 5, 7) and confirm their total. Example: # There are X prime digits.

0 sats \ 0 replies \ @0xbitcoiner 29 Oct

23 minutes later ....

0 sats \ 1 reply \ @Cotton 29 Oct

sounds a bit like math gymnastics to me. :(

0 sats \ 0 replies \ @south_korea_ln OP 29 Oct

Ain't it fun? :)

0 sats \ 0 replies \ @aliceandthewonderland 29 Oct

In this sentence, the number of occurrences of the digit 0 is 3, of the digit 1 is 2, of the digit 2 is 2, of the digit 3 is 2, of even numbers is 5, of odd numbers is 4, and of prime numbers is 4.

0 sats \ 0 replies \ @Aardvark 29 Oct

Once, once, once, once, once, twice, twice.

😁