ChatGPT vs Gemini for math

Every limit is published. Paid plans also have a monthly fair-use limit on AI cost: Plus $3.75, Pro $7.50, Max $20, Ultra $42, Studio $85. Using every message on your plan at typical sizes stays under it; very large messages and heavy research use it faster. Every limit, explained.

Math: GPT-6.1 Sol passed 5 of 5 and Gemini 3.8 Flash 5 of 5. GPT-6.1 Sol answered 2.7× sooner at the median, 1.8 s against 4.7 s. GPT-6.1 Sol cost 1.7× less, $0.0043 against $0.0071 for the 5 replies. Gemini 3.8 Flash's replies ran 96% longer, in tokens of reply, thinking not counted.

1. 1. A discount, then sales tax

   Everyday. GPT: 4 of 4 models passed, GPT-6 Luna the cheapest at $0.0001 · Gemini: 3 of 3 models passed, Gemini 3.8 Flash the cheapest at $0.0007. The prompt in full.

   GPT-6.1 Sol and Gemini 3.8 Flash both passed this one. GPT-6.1 Sol answered sooner (1.5 s to 2.5 s), and cost about the same; GPT-6.1 Sol wrote 39 tokens of reply, Gemini 3.8 Flash 89.

   • GPT-6.1 Sol

     Passed: Final answer 66: right.

     Discounted price: $80 × 0.75 = $60  
     After sales tax: $60 × 1.10 = $66
     
     Final answer: $66

     402 tokens in, 39 out · 1.5 s · $0.0006 · 1 message on Pro · answered by openai/gpt-6.1-sol via OpenAI · September 29, 2026

   • Gemini 3.8 Flash

     Passed: Final answer 66: right.

     1. Calculate the discount: $80 \times 0.25 = $20.
     2. Calculate the discounted price: $80 - $20 = $60.
     3. Calculate the sales tax: $60 \times 0.10 = $6.
     4. Calculate the total cost: $60 + $6 = $66.
     
     Final answer: $66

     430 tokens in, 89 out · 2.5 s · $0.0007 · 1 message on Pro · answered by google/gemini-3.8-flash via Google · September 27, 2026

2. 2. Pens at 3 for $4

   Everyday. GPT: 3 of 4 models passed, GPT-6.1 Sol the cheapest at $0.0010 · Gemini: 3 of 3 models passed, Gemini 4 Argon the cheapest at $0.0015. The prompt in full.

   GPT-6.1 Sol and Gemini 3.8 Flash both passed this one. GPT-6.1 Sol answered sooner (2.4 s to 4.7 s), and GPT-6.1 Sol's reply cost less ($0.0010 to $0.0017); GPT-6.1 Sol wrote 89 tokens of reply, Gemini 3.8 Flash 114.

   • GPT-6.1 Sol

     Passed: Final answer Buy three 3-pen bundles and one single pen for 13.50.: right.

     Three singles cost $4.50, so each 3-for-$4 bundle saves $0.50. Use as many bundles as possible: 3 bundles give 9 pens, then buy 1 single.
     
     Cost: \(3 \times \$4 + \$1.50 = \$13.50\).
     
     Final answer: Buy three 3-pen bundles and one single pen for $13.50.

     404 tokens in, 127 out (38 of them reasoning) · 2.4 s · $0.0010 · 1 message on Pro · answered by openai/gpt-6.1-sol via OpenAI · September 29, 2026

   • Gemini 3.8 Flash

     Passed: Final answer 3 sets of 3 pens and 1 single pen for 13.50: right.

     To get exactly 10 pens at the lowest cost, buy as many 3-pen deals as possible:
     
     * 3 deals of 3 pens = 9 pens for $12.00 ($4.00 × 3)
     * 1 single pen = 1 pen for $1.50
     
     Total cost: $12.00 + $1.50 = $13.50
     
     Final answer: 3 sets of 3 pens and 1 single pen for $13.50

     431 tokens in, 354 out (240 of them reasoning) · 4.7 s · $0.0017 · 1 message on Pro · answered by google/gemini-3.8-flash via Google · September 27, 2026

3. 3. Compound interest over three years

   Everyday. GPT: 4 of 4 models passed, GPT-6 Luna the cheapest at $0.0001 · Gemini: 3 of 3 models passed, Gemini 3.8 Flash the cheapest at $0.0009. The prompt in full.

   GPT-6.1 Sol and Gemini 3.8 Flash both passed this one. GPT-6.1 Sol answered sooner (1.7 s to 2.1 s), and GPT-6.1 Sol's reply cost less ($0.0007 to $0.0009); GPT-6.1 Sol wrote 64 tokens of reply, Gemini 3.8 Flash 148.

   • GPT-6.1 Sol

     Passed: Final answer 315.25: right.

     After 3 years, the balance is:
     \[
     2000(1.05)^3 = \$2,315.25
     \]
     
     Interest earned:
     \[
     \$2,315.25 - \$2,000 = \$315.25
     \]
     
     Final answer: $315.25

     404 tokens in, 64 out · 1.7 s · $0.0007 · 1 message on Pro · answered by openai/gpt-6.1-sol via OpenAI · September 29, 2026

   • Gemini 3.8 Flash

     Passed: Final answer 315.25: right.

     To find the total amount $A$ after 3 years:
     $A = P(1 + r)^t$
     $A = 2000 \times (1 + 0.05)^3$
     $A = 2000 \times (1.05)^3$
     $A = 2000 \times 1.157625 = 2315.25$
     
     To find the interest earned:
     $\text{Interest} = A - P = 2315.25 - 2000 = 315.25$
     
     Final answer: $315.25

     429 tokens in, 148 out · 2.1 s · $0.0009 · 1 message on Pro · answered by google/gemini-3.8-flash via Google · September 27, 2026

4. 4. Four-digit numbers whose digits sum to 9

   Hard. GPT: 4 of 4 models passed, GPT-6 Luna the cheapest at $0.0001 · Gemini: 3 of 3 models passed, Gemini 4 Argon the cheapest at $0.0020. The prompt in full.

   GPT-6.1 Sol and Gemini 3.8 Flash both passed this one. GPT-6.1 Sol answered sooner (2.7 s to 4.7 s), and GPT-6.1 Sol's reply cost less ($0.0011 to $0.0022); GPT-6.1 Sol wrote 108 tokens of reply, Gemini 3.8 Flash 235.

   • GPT-6.1 Sol

     Passed: Final answer 165: right.

     Let the digits be \(a,b,c,d\), with \(a\ge1\). Set \(x=a-1\). Then
     \[
     x+b+c+d=8,
     \]
     where all four variables are nonnegative. Each resulting digit is automatically at most 9.
     
     By stars and bars, the number of solutions is
     \[
     \binom{8+4-1}{4-1}=\binom{11}{3}=165.
     \]
     
     Final answer: 165

     380 tokens in, 147 out (39 of them reasoning) · 2.7 s · $0.0011 · 1 message on Pro · answered by openai/gpt-6.1-sol via OpenAI · September 29, 2026

   • Gemini 3.8 Flash

     Passed: Final answer 165: right.

     Let the four digits be represented by $a, b, c,$ and $d$, where $a \in \{1, 2, \dots, 9\}$ and $b, c, d \in \{0, 1, \dots, 9\}$.
     
     We need to find the number of integer solutions to:
     $$a + b + c + d = 9$$
     
     Let $a' = a - 1$ so that $a' \ge 0$. Substituting gives:
     $$a' + b + c + d = 8$$
     
     Since the sum is $8$, no individual variable can exceed $8$, so the constraint that digits must be $\le 9$ is automatically satisfied.
     
     Using the stars and bars formula, the number of non-negative integer solutions is:
     $$\binom{8 + 4 - 1}{4 - 1} = \binom{11}{3} = \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165$$
     
     Final answer: 165

     404 tokens in, 495 out (260 of them reasoning) · 4.7 s · $0.0022 · 1 message on Pro · answered by google/gemini-3.8-flash via Google · September 27, 2026

5. 5. The highest of three dice is a 5

   Hard. GPT: 4 of 4 models passed, GPT-6 Luna the cheapest at $0.0001 · Gemini: 3 of 3 models passed, Gemini 4 Argon the cheapest at $0.0016. The prompt in full.

   GPT-6.1 Sol and Gemini 3.8 Flash both passed this one. GPT-6.1 Sol answered sooner (1.8 s to 4.9 s), and GPT-6.1 Sol's reply cost less ($0.0008 to $0.0018); GPT-6.1 Sol wrote 87 tokens of reply, Gemini 3.8 Flash 172.

   • GPT-6.1 Sol

     Passed: Final answer (61/216 ): right.

     The highest number is exactly 5 if all three dice show at most 5, but not all show at most 4.
     
     \[
     P(\max=5)=\left(\frac56\right)^3-\left(\frac46\right)^3
     =\frac{125-64}{216}=\frac{61}{216}.
     \]
     
     Final answer: \(\frac{61}{216}\)

     395 tokens in, 87 out · 1.8 s · $0.0008 · 1 message on Pro · answered by openai/gpt-6.1-sol via OpenAI · September 29, 2026

   • Gemini 3.8 Flash

     Passed: Final answer 61/216: right.

     To find the probability that the highest number showing on three fair six-sided dice is exactly 5:
     
     1. The total number of possible outcomes when rolling three dice is $6^3 = 216$.
     2. The number of outcomes where all three dice show a number less than or equal to 5 is $5^3 = 125$.
     3. The number of outcomes where all three dice show a number less than or equal to 4 (meaning no 5 is rolled) is $4^3 = 64$.
     4. The number of outcomes where the maximum number is exactly 5 is $125 - 64 = 61$.
     
     Thus, the probability is $\frac{61}{216}$.
     
     Final answer: 61/216

     421 tokens in, 392 out (220 of them reasoning) · 4.9 s · $0.0018 · 1 message on Pro · answered by google/gemini-3.8-flash via Google · September 27, 2026

• GPT-6 Astra vs Gemini 4 Argon: 5 of 5 each; GPT-6 Astra answered 1.7× sooner at the median and Gemini 4 Argon cost 5.5× less. Gemini 4 Argon vs GPT-6 Astra, on every job.

• GPT-6 Astra vs Gemini 3.1 Pro: 5 of 5 each; GPT-6 Astra answered 3.2× sooner at the median and cost 1.2× less.

• GPT-6 Astra vs Gemini 3.8 Flash: 5 of 5 each; GPT-6 Astra answered 1.8× sooner at the median and Gemini 3.8 Flash cost 6.0× less.

• GPT-6.1 Sol vs Gemini 4 Argon: 5 of 5 each; GPT-6.1 Sol answered 2.5× sooner at the median and cost 1.8× less. Gemini 4 Argon vs GPT-6.1 Sol, on every job.

• GPT-6.1 Sol vs Gemini 3.1 Pro: 5 of 5 each; GPT-6.1 Sol answered 4.7× sooner at the median and cost 11.6× less.

• GPT-6.1 Sol vs Gemini 3.8 Flash: 5 of 5 each; GPT-6.1 Sol answered 2.7× sooner at the median and cost 1.7× less.

• GPT-6 Sol vs Gemini 4 Argon: 5 of 5 each; GPT-6 Sol answered 2.0× sooner at the median and Gemini 4 Argon cost 1.2× less.

• GPT-6 Sol vs Gemini 3.1 Pro: 5 of 5 each; GPT-6 Sol answered 3.8× sooner at the median and cost 5.5× less. GPT-6 Sol vs Gemini 3.1 Pro (preview), on every job.

• GPT-6 Sol vs Gemini 3.8 Flash: 5 of 5 each; GPT-6 Sol answered 2.2× sooner at the median and Gemini 3.8 Flash cost 1.3× less. GPT-6 Sol vs Gemini 3.8 Flash, on every job.

• GPT-6 Luna vs Gemini 4 Argon: GPT-6 Luna 4 of 5, Gemini 4 Argon 5; GPT-6 Luna answered 2.0× sooner at the median and cost 15.7× less.

• GPT-6 Luna vs Gemini 3.1 Pro: GPT-6 Luna 4 of 5, Gemini 3.1 Pro 5; GPT-6 Luna answered 3.8× sooner at the median and cost 101.7× less.

• GPT-6 Luna vs Gemini 3.8 Flash: GPT-6 Luna 4 of 5, Gemini 3.8 Flash 5; GPT-6 Luna answered 2.1× sooner at the median and cost 14.5× less. GPT-6 Luna vs Gemini 3.8 Flash, on every job.

Every GPT and Gemini reply above was checked the same way as every other model's, by the rules published with the prompts: how the math prompts are scored, and each one in full.

• The lineups

  GPT: 4 models, GPT-6 Astra, GPT-6.1 Sol, GPT-6 Sol, and GPT-6 Luna. Gemini: 3 models, Gemini 4 Argon, Gemini 3.1 Pro (preview), and Gemini 3.8 Flash.

• Price per message

  The least expensive GPT model is GPT-6 Luna (60 messages a day on Pro); the least expensive Gemini model is Gemini 3.8 Flash (250 messages a month on Pro).

• Context window

  GPT goes up to 1.05M tokens (GPT-6 Astra); Gemini up to 1.05M tokens (Gemini 4 Argon).

• Images and PDFs

  Every model here reads images. Every model here takes a PDF as a whole file.

• On the Free plan

  None of these models is on the Free plan. Paid plans have them, with messages every month: GPT-6 Astra from Pro up.

In llmwise, a message to GPT or Gemini goes to the model's maker, or through OpenRouter when llmwise can't reach the maker directly. The Privacy Policy has the details.