doubtful_sentence string | problem_id string | model_name string | intervention_type string | timestep int64 | continuation_index int64 | verifier_score int64 |
|---|---|---|---|---|---|---|
Wait, perhaps I'm overcomplicating. | 700415 | DeepSeek-R1-Distill-Llama-8B | neutral_add_random_text | 30 | 3 | 1 |
Hmm, but self-complementary graphs have specific properties, but I'm not sure. | 700415 | DeepSeek-R1-Distill-Llama-8B | neutral_add_random_text | 30 | 3 | 1 |
Alternatively, if the graph is regular, maybe? | 700415 | DeepSeek-R1-Distill-Llama-8B | neutral_add_random_text | 30 | 3 | 1 |
Wait, no, that's not relevant here. | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
Let me refocus. | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
So, the distance between 31 and 7 is equal to the distance between 31 and 14. | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
So, maybe it's not the minimal distance, but the distance in one direction? | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
Or maybe it's considering the absolute difference in numbering? | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
Wait, perhaps it's better to model this as a circle. | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
But actually, the problem says person 1 has card 1, and the rest have cards 2, 3, etc., | 394355 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 2 | 1 |
So, the problem reduces to finding all ordered pairs (A, B) where A is from 1 to 9, B is from 0 to 9, and A + B is from 0 to 9. | 331547 | DeepSeek-R1-Distill-Qwen-14B | neutral_insert_random_characters | 10 | 3 | 1 |
Wait, but according to the previous analysis, it's -1. | 334795 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_insert_wrong_fact | 90 | 8 | 1 |
Wait, but maybe I made a mistake in the approximation. | 334795 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_insert_wrong_fact | 90 | 8 | 1 |
Wait, let me check again. | 334795 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_insert_wrong_fact | 90 | 8 | 1 |
So numerator≈31.72 -999.9975≈-968.2775 | 334795 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_insert_wrong_fact | 90 | 8 | 1 |
sqrt(10^12 -5)≈10^6 - negligible. | 334795 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_insert_wrong_fact | 90 | 8 | 1 |
So numerator≈1000.003 -10^6≈-999,999.997 | 334795 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_insert_wrong_fact | 90 | 8 | 1 |
Wait, is that correct? | 711012 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_insert_wrong_fact | 90 | 4 | 1 |
Wait, no, that's not right. | 711012 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_insert_wrong_fact | 90 | 4 | 1 |
Because \( z^3 = 39 + 26i \), so \( a^3 - 3ab^2 + 3a^2b - b^3i = 39 + 26i \). | 711012 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_insert_wrong_fact | 90 | 4 | 1 |
Wait, that's not how we derived earlier. | 711012 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_insert_wrong_fact | 90 | 4 | 1 |
So, \( |z| = (13 \sqrt{13})^{1/3} = 13^{1/2} \), which is \( \sqrt{13} \). | 711012 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_insert_wrong_fact | 90 | 4 | 1 |
Wait, that's about asteroid discovery, not my math problem. | 580454 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 1 | 1 |
So, \( f(x - 1) \approx f(x) - f'(x) \cdot 1 = \sqrt{x} - \frac{1}{2\sqrt{x}} \). | 580454 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 1 | 1 |
Wait, is that true? | 597350 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
Wait, maybe I should think differently. | 597350 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
18!)/2 = (17! * | 597350 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
S = (31! * | 597350 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
32!)/2 = (31! * | 597350 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
50!)/2 = (49! * | 597350 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
Wait, is that correct? | 413736 | DeepSeek-R1-Distill-Llama-8B | adversarial_insert_wrong_fact | 30 | 7 | 1 |
Wait, no, that's not exactly right. | 413736 | DeepSeek-R1-Distill-Llama-8B | adversarial_insert_wrong_fact | 30 | 7 | 1 |
The expansion of \( (a + b + c)^3 \) is:
\( (a + b + c)^3 = a^3 + b^3 + c^3 + 3(a + b)(b + c)(a + c) \). | 413736 | DeepSeek-R1-Distill-Llama-8B | adversarial_insert_wrong_fact | 30 | 7 | 1 |
Hmm, that doesn't seem helpful. | 413736 | DeepSeek-R1-Distill-Llama-8B | adversarial_insert_wrong_fact | 30 | 7 | 1 |
Wait, maybe another approach. | 413736 | DeepSeek-R1-Distill-Llama-8B | adversarial_insert_wrong_fact | 30 | 7 | 1 |
Wait, hold on: \( 333(a + b + c) = 333*(-1) = -333 \). | 413736 | DeepSeek-R1-Distill-Llama-8B | adversarial_insert_wrong_fact | 30 | 7 | 1 |
But perhaps that's irrelevant here. | 467556 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 8 | 1 |
Wait, perhaps I need to check if there are any other factor pairs where both are odd. | 467556 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 8 | 1 |
So, only factor pairs where both are even are valid, which we have already considered. | 467556 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 8 | 1 |
Wait, no, I was talking about the independent set. | 552264 | DeepSeek-R1-Distill-Qwen-7B | adversarial_continue_unrelated | 90 | 6 | 1 |
But primes in B are numbers like 51, 52, ..., 100. | 552264 | DeepSeek-R1-Distill-Qwen-7B | adversarial_continue_unrelated | 90 | 6 | 1 |
Wait, no, that's not right because the total number of girls is 35, not the number of girls in a single class. | 555988 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 90 | 7 | 1 |
Wait, maybe I confused something here. | 555988 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 90 | 7 | 1 |
Wait, hold on, the problem says Class 4(2) has 19 boys, but it doesn't specify the total number of students in Class 4(2). | 555988 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 90 | 7 | 1 |
Wait, so both classes have 36 students each? | 555988 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 90 | 7 | 1 |
That's not what the problem said. | 555988 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_with_wrong_reasoning | 90 | 7 | 1 |
Wait, wait, no, 9K/4 = 36, so K = 36 * 4 /9 = 16. | 504894 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 70 | 4 | 1 |
Wait, but let me check the first part again. | 504894 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 70 | 4 | 1 |
Wait, but I thought maybe I made a mistake in the equations. | 504894 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 70 | 4 | 1 |
Let me try again. | 504894 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 70 | 4 | 1 |
Moreover, the wall has been a subject of many myths and legends. | 762703 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 90 | 7 | 1 |
Wait, no, that's incorrect. | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
Let me correct that. | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
0.45 * 0.70: 45 * 70 = 3150. | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
Since both numbers have two decimal places, the result should have four decimal places, which is 0.3150. | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
Wait, but 0.45 * 0.70 is equal to 0.315, not 3.15. | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
So, I made a mistake earlier. | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
Let me correct that: | 507992 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 10 | 5 | 1 |
Wait, is that possible? | 434479 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
So, if \( EF \) is the diagonal, then \( EF = \sqrt{2} \), so perimeter would be \( 1 + 1 + \sqrt{2} = 2 + \sqrt{2} \). | 434479 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
Alternatively, perhaps the perimeter is fixed at \( 2 + \sqrt{2} \), so I can just compute that. | 434479 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
But wait, in our earlier attempt, the only solution was the degenerate case, but maybe in reality, the perimeter is fixed, and the triangle is such that \( EF \) is the diagonal. | 434479 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
Wait, perhaps the perimeter is \( 2 + \sqrt{2} \). | 434479 | DeepSeek-R1-Distill-Qwen-1_5B | adversarial_continue_with_wrong_reasoning | 70 | 6 | 1 |
Hmm, but that's a different topic. | 676437 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 70 | 4 | 1 |
Wait, no, back to the problem. | 676437 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 70 | 4 | 1 |
5 divided by 9 is approximately 0.555... kilograms. | 458736 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 10 | 7 | 1 |
Wait, that doesn't seem right. | 458736 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 10 | 7 | 1 |
Wait, maybe I'm confusing the ratio. | 458736 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 10 | 7 | 1 |
Wait, no, that would mean 1 part is 5 kg, so 9 parts would be 45 kg. | 458736 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 10 | 7 | 1 |
Wait, that seems high. | 458736 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 10 | 7 | 1 |
Wait, but the answer choices don't have 45 as the correct answer? | 458736 | Llama-3_1-Nemotron-Nano-8B-v1 | adversarial_continue_with_wrong_reasoning | 10 | 7 | 1 |
Breaking it down:
- \( 1990 = 2000 - 10 \)
- Therefore, \( (2000 - 10)^2 = 2000^2 - 2 \times 2000 \times 10 + 10^2 = 4,000,000 - 40,000 + 100 = 3,960,100 \)
- Adding 1 to this gives \( 3,960,101 \) | 769982 | DeepSeek-R1-Distill-Qwen-7B | benign_rewrite_trace | 10 | 5 | 1 |
Summing the digits of 401:
- 4 + 0 + 1 = 5 | 769982 | DeepSeek-R1-Distill-Qwen-7B | benign_rewrite_trace | 10 | 5 | 1 |
Summing the digits of 26:
- 2 + 6 = 8 | 769982 | DeepSeek-R1-Distill-Qwen-7B | benign_rewrite_trace | 10 | 5 | 1 |
Summing the digits of 65:
- 6 + 5 = 11 | 769982 | DeepSeek-R1-Distill-Qwen-7B | benign_rewrite_trace | 10 | 5 | 1 |
Summing the digits of 122:
- 1 + 2 + 2 = 5 | 769982 | DeepSeek-R1-Distill-Qwen-7B | benign_rewrite_trace | 10 | 5 | 1 |
So, I'm a bit confused because the first part of the message seems to be about a math problem, and then it jumps into agricultural experiments. | 574993 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 3 | 1 |
So, instead of 3 times x, which is 90, he does x divided by 3. | 574993 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 3 | 1 |
Looking at the options, B is 10, so that must be the answer. | 574993 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 3 | 1 |
Wait, let me double-check. | 574993 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 3 | 1 |
But hold on, let me make sure I didn't misinterpret the question. | 574993 | DeepSeek-R1-Distill-Qwen-14B | neutral_add_random_text | 10 | 3 | 1 |
Wait, that's way off track. | 711012 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 6 | 1 |
1. \( ( | 711012 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 6 | 1 |
-1/2)Q^3 + (3/2)Q R^2 = 65 \)
2. \( ( | 711012 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 6 | 1 |
1. \( ( | 711012 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 6 | 1 |
1/2)(-Q^3 + 3Q R^2) = 65 \) => \( -Q^3 + 3Q R^2 = 130 \)
2. \( ( | 711012 | DeepSeek-R1-Distill-Qwen-14B | adversarial_continue_unrelated | 50 | 6 | 1 |
Wait, maybe I should think in terms of coordinates. | 421500 | DeepSeek-R1-Distill-Qwen-14B | adversarial_insert_wrong_fact | 30 | 4 | 1 |
Take absolute value and divide by 2: |a²/2| / 2 = (a²/2)/2 = a²/4 | 421500 | DeepSeek-R1-Distill-Qwen-14B | adversarial_insert_wrong_fact | 30 | 4 | 1 |
Wait, no, that doesn't seem right. | 699043 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_with_wrong_reasoning | 50 | 3 | 1 |
Wait, perhaps the confusion arises from different approaches. | 699043 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_with_wrong_reasoning | 50 | 3 | 1 |
Wait, now I have two different answers: 40 and 20. | 699043 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_with_wrong_reasoning | 50 | 3 | 1 |
Wait, no, hold on. | 699043 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_with_wrong_reasoning | 50 | 3 | 1 |
So, the probability that the error is not exceeding 15 mm is the probability that Z ≤ 15, where Z is the Z-score. | 332342 | DeepSeek-R1-Distill-Llama-8B | neutral_add_random_text | 10 | 2 | 0 |
But wait, let me double-check that. | 332342 | DeepSeek-R1-Distill-Llama-8B | neutral_add_random_text | 10 | 2 | 0 |
[B]
1900 – Charles Darwin, English naturalist and geographer (d. 1923)
1902 – Daniel Tamson, British lawyer, politician, and educationist (d. 1973)
1903 – Arthur Mersenne, French scientist and mathematician (d. 1915)
1907 – Leopold Pochard, German botanist and geologist (d. 1910)
1912 – John Chisholm, British geographe... | 431680 | DeepSeek-R1-Distill-Qwen-1_5B | neutral_add_random_text | 50 | 3 | 0 |
So, Charles Darwin was alive until 1923, so the last significant date is 1923. | 431680 | DeepSeek-R1-Distill-Qwen-1_5B | neutral_add_random_text | 50 | 3 | 0 |
So, the problem is about Charles Darwin's life, but in the problem, it's just a geometry problem with the given medians. | 431680 | DeepSeek-R1-Distill-Qwen-1_5B | neutral_add_random_text | 50 | 3 | 0 |
But anyway, perhaps I can go back to the formula. | 431680 | DeepSeek-R1-Distill-Qwen-1_5B | neutral_add_random_text | 50 | 3 | 0 |
Wait, but perhaps in the problem, the lengths of the medians are given, but in reality, Charles Darwin's life span is until 1923, but in the problem, it's just a geometry problem, so maybe the values are hypothetical. | 431680 | DeepSeek-R1-Distill-Qwen-1_5B | neutral_add_random_text | 50 | 3 | 0 |
Hmm, but that's a different topic. | 558369 | DeepSeek-R1-Distill-Llama-8B | adversarial_continue_unrelated | 10 | 4 | 1 |
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