DeepSeek 又一轮砸盘来了， 人工智能图形处理软件JANUS 也开源了

[ogygia]

chatgpt-4 turbo 只用了几秒钟就 给出了正确答案。

 

[ogygia]

Find the number of ordered pairs of integers (a,b) such that the sequence 3,4,5,a,b,30,40,50 is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.

ChatGPT said:​

To solve this problem, we need to find all possible ordered pairs (a,b)(a, b)(a,b) such that the sequence

3,4,5,a,b,30,40,503, 4, 5, a, b, 30, 40, 503,4,5,a,b,30,40,50

satisfies two conditions:

1. The sequence is strictly increasing.
2. No subset of four terms (not necessarily consecutive) forms an arithmetic progression.

Step 1: Strictly Increasing Condition​

Since the sequence is strictly increasing, we must have:

5<a<b<30.5 < a < b < 30.5<a<b<30.
Thus, aaa and bbb must be integers satisfying:

a∈{6,7,…,29},b∈{a+1,a+2,…,29}.a \in \{6, 7, \ldots, 29\}, \quad b \in \{a+1, a+2, \ldots, 29\}.a∈{6,7,…,29},b∈{a+1,a+2,…,29}.
This gives b−ab - ab−a possible values for bbb for each valid aaa. We'll revisit this after considering the second condition.

---

Step 2: No Arithmetic Progression of Four Terms​

An arithmetic progression of four terms satisfies:

x1,x2,x3,x4withx2−x1=x3−x2=x4−x3.x_1, x_2, x_3, x_4 \quad \text{with} \quad x_2 - x_1 = x_3 - x_2 = x_4 - x_3.x1,x2,x3,x4withx2−x1=x3−x2=x4−x3.
We need to ensure that no such progression exists for any subset of {3,4,5,a,b,30,40,50}\{3, 4, 5, a, b, 30, 40, 50\}{3,4,5,a,b,30,40,50}. The fixed terms 3,4,5,30,40,503, 4, 5, 30, 40, 503,4,5,30,40,50 cannot form an arithmetic progression of four terms themselves. So, we need to carefully place aaa and bbb to avoid creating progressions.

Step 2.1: Common Differences in the Fixed Terms​

We analyze the fixed terms {3,4,5,30,40,50}\{3, 4, 5, 30, 40, 50\}{3,4,5,30,40,50} and their possible differences:

• Differences between consecutive terms: 4−3=14 - 3 = 14−3=1, 5−4=15 - 4 = 15−4=1, 30−5=2530 - 5 = 2530−5=25, 40−30=1040 - 30 = 1040−30=10, 50−40=1050 - 40 = 1050−40=10.
• We must ensure aaa and bbb do not create a four-term arithmetic progression involving any subset of these terms.

Step 2.2: Constraints on​

• aaa cannot be placed such that it creates an arithmetic progression with 3,4,53, 4, 53,4,5 or 30,40,5030, 40, 5030,40,50.
• For example:
  • If a=15a = 15a=15, then {3,9,15,21}\{3, 9, 15, 21\}{3,9,15,21} forms an arithmetic progression, which is not allowed.
  • Similarly, bbb must avoid creating progressions when paired with any three other terms.

---

Step 3: Systematic Counting of Valid Pairs​

To solve this rigorously, we would need to:

1. Identify all subsets of size 4 from {3,4,5,a,b,30,40,50}\{3, 4, 5, a, b, 30, 40, 50\}{3,4,5,a,b,30,40,50}.
2. For each subset, check whether it forms an arithmetic progression.
3. Exclude all (a,b)(a, b)(a,b) that lead to any arithmetic progression.

This process is complex and computationally intensive. However, if you'd like, I can implement a programmatic solution to enumerate and verify all pairs (a,b)(a, b)(a,b). Would you like me to proceed?

You said:​

Yes

ChatGPT said:​

There are 228 valid ordered pairs (a,b)(a, b)(a,b) such that the sequence 3,4,5,a,b,30,40,503, 4, 5, a, b, 30, 40, 503,4,5,a,b,30,40,50 is strictly increasing and no subset of four terms forms an arithmetic progression.

Here are the first 10 valid pairs for verification:

(7, 8), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18)

 

[ogygia]

又测了一题 (1989 AIME #7)：
If the integer k is added to each of the numbers 36, 300, and 596, one obtains the squares of three consecutive terms of an arithmetic series. Find k.
Answer: 925

deepseek R1 和 chatgpt 4 turbo 都能给出正确答案。

 

[向问天]

用deepseek R1测了一道 AIME (2022 AIME I #6)：

American Invitational Mathematics Examination - Wikipedia

en.wikipedia.org

Find the number of ordered pairs of integers (a,b) such that the sequence 3,4,5,a,b,30,40,50 is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.
Answer: 228

deepseek R1算了10多分钟，得出结果是 10.
整个一个瞎蒙。

我的 DeepSeek 得238

 

[向问天]

ChatGpt 得不出确定的数字

 

[向问天]

Grok2 的答案是475

 

[ogygia]

what is the version of chatgpt?

 

[metropolis]

又测了一题 (1989 AIME #7)：
If the integer k is added to each of the numbers 36, 300, and 596, one obtains the squares of three consecutive terms of an arithmetic series. Find k.
Answer: 925

deepseek R1 和 chatgpt 4 turbo 都能给出正确答案。

这道题我用Grok2得出的答案是k=13

 

[billwanhua]

Find the number of ordered pairs of integers (a,b) such that the sequence 3,4,5,a,b,30,40,50 is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.

ChatGPT said:​

To solve this problem, we need to find all possible ordered pairs (a,b)(a, b)(a,b) such that the sequence

3,4,5,a,b,30,40,503, 4, 5, a, b, 30, 40, 503,4,5,a,b,30,40,50

satisfies two conditions:

1. The sequence is strictly increasing.
2. No subset of four terms (not necessarily consecutive) forms an arithmetic progression.

Step 1: Strictly Increasing Condition​

Since the sequence is strictly increasing, we must have:

5<a<b<30.5 < a < b < 30.5<a<b<30.
Thus, aaa and bbb must be integers satisfying:

a∈{6,7,…,29},b∈{a+1,a+2,…,29}.a \in \{6, 7, \ldots, 29\}, \quad b \in \{a+1, a+2, \ldots, 29\}.a∈{6,7,…,29},b∈{a+1,a+2,…,29}.
This gives b−ab - ab−a possible values for bbb for each valid aaa. We'll revisit this after considering the second condition.

---

Step 2: No Arithmetic Progression of Four Terms​

An arithmetic progression of four terms satisfies:

x1,x2,x3,x4withx2−x1=x3−x2=x4−x3.x_1, x_2, x_3, x_4 \quad \text{with} \quad x_2 - x_1 = x_3 - x_2 = x_4 - x_3.x1,x2,x3,x4withx2−x1=x3−x2=x4−x3.
We need to ensure that no such progression exists for any subset of {3,4,5,a,b,30,40,50}\{3, 4, 5, a, b, 30, 40, 50\}{3,4,5,a,b,30,40,50}. The fixed terms 3,4,5,30,40,503, 4, 5, 30, 40, 503,4,5,30,40,50 cannot form an arithmetic progression of four terms themselves. So, we need to carefully place aaa and bbb to avoid creating progressions.

Step 2.1: Common Differences in the Fixed Terms​

We analyze the fixed terms {3,4,5,30,40,50}\{3, 4, 5, 30, 40, 50\}{3,4,5,30,40,50} and their possible differences:

• Differences between consecutive terms: 4−3=14 - 3 = 14−3=1, 5−4=15 - 4 = 15−4=1, 30−5=2530 - 5 = 2530−5=25, 40−30=1040 - 30 = 1040−30=10, 50−40=1050 - 40 = 1050−40=10.
• We must ensure aaa and bbb do not create a four-term arithmetic progression involving any subset of these terms.

Step 2.2: Constraints on​

• aaa cannot be placed such that it creates an arithmetic progression with 3,4,53, 4, 53,4,5 or 30,40,5030, 40, 5030,40,50.
• For example:
  • If a=15a = 15a=15, then {3,9,15,21}\{3, 9, 15, 21\}{3,9,15,21} forms an arithmetic progression, which is not allowed.
  • Similarly, bbb must avoid creating progressions when paired with any three other terms.

---

Step 3: Systematic Counting of Valid Pairs​

To solve this rigorously, we would need to:

1. Identify all subsets of size 4 from {3,4,5,a,b,30,40,50}\{3, 4, 5, a, b, 30, 40, 50\}{3,4,5,a,b,30,40,50}.
2. For each subset, check whether it forms an arithmetic progression.
3. Exclude all (a,b)(a, b)(a,b) that lead to any arithmetic progression.

This process is complex and computationally intensive. However, if you'd like, I can implement a programmatic solution to enumerate and verify all pairs (a,b)(a, b)(a,b). Would you like me to proceed?

You said:​

Yes

ChatGPT said:​

There are 228 valid ordered pairs (a,b)(a, b)(a,b) such that the sequence 3,4,5,a,b,30,40,503, 4, 5, a, b, 30, 40, 503,4,5,a,b,30,40,50 is strictly increasing and no subset of four terms forms an arithmetic progression.

Here are the first 10 valid pairs for verification:

(7, 8), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18)

这种不属于解答，程序列举法，任何计算机都可以，虽然答案对，你如果让DS 写程序计算，会很快得出结论

 

[ogygia]

这种不属于解答，程序列举法，任何计算机都可以，虽然答案对，你如果让DS 写程序计算，会很快得出结论

你能给deepseek R1 多重prompts 引导它给出正确答案吗？包括用多重prompts让DS 写程序计算。

 

[billwanhua]

你能给deepseek R1 多重prompts 引导它给出正确答案吗？包括用多重prompts让DS 写程序计算。

一秒钟，给出程序你可以运行。
你自己可以问：
can you write a program to solve it

初学者程序而已

 

[ogygia]

只要能用多重prompts能解决问题，就很好。
如果不能给出答案，最好不好误导。

 

[billwanhua]

你要知道如何问问题，你如果只需要结论，很容易得出，如果需要解题思路，那又是另外一回事。

这种题目，没有人需要答案吧，答案只是验证你思路是不是正确

如果给我纸笔，我也很容易给出答案，时间而已

 

[ogygia]

"Chain of thought" 是推理的最基础功能

 

[metropolis]

黄仁勋对DS的看法 - 金溇银澧发表于 投资理财 - 论坛 | 文学城

bbs.wenxuecity.com

真假不知