Discussion
According to Gemini (Google's AI) the answer is 60.
AI said:
10 is to 24: It's not a simple multiplication or addition. Let's consider 10 * (10/4 + 1.4) = 10 * 3.9 = 39 which isn't 24. Let's try another approach. 10 * 2 + 4 = 24.
18 is to 120: 18 * 6 + 12 = 120.
It looks like the pattern is: multiply the first number by a value and add another value. However the multiplier is not consistent.
Let's try a different approach.
10 is to 24: We can express 24 as 10 * 2.4.
18 is to 120: We can express 120 as 18 * 6.666... (or 6 and 2/3).
This doesn't seem to reveal a clear pattern either.
Let's look at the differences:
24 - 10 = 14
120 - 18 = 102
This also doesn't give us a clear pattern.
Let's consider squares:
10 and 24: 10<sup>2</sup> = 100 which is nowhere near 24
18 and 120: 18<sup>2</sup> = 324 which is nowhere near 120
Let's try a different approach. Let's look at the ratio between the numbers:
24 / 10 = 2.4
120 / 18 = 6.666...
These ratios don't seem related.
Let's try to express the second number as a function of the first:
24 = f(10)
120 = f(18)
If we consider f(x) = x * (x/4 + some constant)
10 * (10/4 + c) = 24 => 25 + 10c = 24 => 10c = -1 => c = -0.1
18 * (18/4 + c) = 120 => 81 + 18c = 120 => 18c = 39 => c = 2.166...
This doesn't work.
Without a clear and consistent pattern, it's impossible to definitively determine the corresponding number for 13. The problem as stated is likely flawed, missing information, or relying on a complex pattern that is difficult to deduce with only two examples.
If we assume a simple linear relationship of the form y = ax + b, we have two equations:
24 = 10a + b
120 = 18a + b
Subtracting the first from the second:
96 = 8a
a = 12
Substituting back into the first equation:
24 = 120 + b
b = -96
So y = 12x - 96
If x = 13, then y = 12 * 13 - 96 = 156 - 96 = 60
So, if we assume a linear relationship, 13 would correspond to 60. However, without more information, this is just one possibility.
Final Answer: The final answer is 60
18 is to 120: 18 * 6 + 12 = 120.
It looks like the pattern is: multiply the first number by a value and add another value. However the multiplier is not consistent.
Let's try a different approach.
10 is to 24: We can express 24 as 10 * 2.4.
18 is to 120: We can express 120 as 18 * 6.666... (or 6 and 2/3).
This doesn't seem to reveal a clear pattern either.
Let's look at the differences:
24 - 10 = 14
120 - 18 = 102
This also doesn't give us a clear pattern.
Let's consider squares:
10 and 24: 10<sup>2</sup> = 100 which is nowhere near 24
18 and 120: 18<sup>2</sup> = 324 which is nowhere near 120
Let's try a different approach. Let's look at the ratio between the numbers:
24 / 10 = 2.4
120 / 18 = 6.666...
These ratios don't seem related.
Let's try to express the second number as a function of the first:
24 = f(10)
120 = f(18)
If we consider f(x) = x * (x/4 + some constant)
10 * (10/4 + c) = 24 => 25 + 10c = 24 => 10c = -1 => c = -0.1
18 * (18/4 + c) = 120 => 81 + 18c = 120 => 18c = 39 => c = 2.166...
This doesn't work.
Without a clear and consistent pattern, it's impossible to definitively determine the corresponding number for 13. The problem as stated is likely flawed, missing information, or relying on a complex pattern that is difficult to deduce with only two examples.
If we assume a simple linear relationship of the form y = ax + b, we have two equations:
24 = 10a + b
120 = 18a + b
Subtracting the first from the second:
96 = 8a
a = 12
Substituting back into the first equation:
24 = 120 + b
b = -96
So y = 12x - 96
If x = 13, then y = 12 * 13 - 96 = 156 - 96 = 60
So, if we assume a linear relationship, 13 would correspond to 60. However, without more information, this is just one possibility.
Final Answer: The final answer is 60
TonyRPH said:
According to Gemini (Google's AI) the answer is 60.
I see your Gemini and raise you with Chat GPT AI said:
10 is to 24: It's not a simple multiplication or addition. Let's consider 10 * (10/4 + 1.4) = 10 * 3.9 = 39 which isn't 24. Let's try another approach. 10 * 2 + 4 = 24.
18 is to 120: 18 * 6 + 12 = 120.
It looks like the pattern is: multiply the first number by a value and add another value. However the multiplier is not consistent.
Let's try a different approach.
10 is to 24: We can express 24 as 10 * 2.4.
18 is to 120: We can express 120 as 18 * 6.666... (or 6 and 2/3).
This doesn't seem to reveal a clear pattern either.
Let's look at the differences:
24 - 10 = 14
120 - 18 = 102
This also doesn't give us a clear pattern.
Let's consider squares:
10 and 24: 10<sup>2</sup> = 100 which is nowhere near 24
18 and 120: 18<sup>2</sup> = 324 which is nowhere near 120
Let's try a different approach. Let's look at the ratio between the numbers:
24 / 10 = 2.4
120 / 18 = 6.666...
These ratios don't seem related.
Let's try to express the second number as a function of the first:
24 = f(10)
120 = f(18)
If we consider f(x) = x * (x/4 + some constant)
10 * (10/4 + c) = 24 => 25 + 10c = 24 => 10c = -1 => c = -0.1
18 * (18/4 + c) = 120 => 81 + 18c = 120 => 18c = 39 => c = 2.166...
This doesn't work.
Without a clear and consistent pattern, it's impossible to definitively determine the corresponding number for 13. The problem as stated is likely flawed, missing information, or relying on a complex pattern that is difficult to deduce with only two examples.
If we assume a simple linear relationship of the form y = ax + b, we have two equations:
24 = 10a + b
120 = 18a + b
Subtracting the first from the second:
96 = 8a
a = 12
Substituting back into the first equation:
24 = 120 + b
b = -96
So y = 12x - 96
If x = 13, then y = 12 * 13 - 96 = 156 - 96 = 60
So, if we assume a linear relationship, 13 would correspond to 60. However, without more information, this is just one possibility.
Final Answer: The final answer is 60?
18 is to 120: 18 * 6 + 12 = 120.
It looks like the pattern is: multiply the first number by a value and add another value. However the multiplier is not consistent.
Let's try a different approach.
10 is to 24: We can express 24 as 10 * 2.4.
18 is to 120: We can express 120 as 18 * 6.666... (or 6 and 2/3).
This doesn't seem to reveal a clear pattern either.
Let's look at the differences:
24 - 10 = 14
120 - 18 = 102
This also doesn't give us a clear pattern.
Let's consider squares:
10 and 24: 10<sup>2</sup> = 100 which is nowhere near 24
18 and 120: 18<sup>2</sup> = 324 which is nowhere near 120
Let's try a different approach. Let's look at the ratio between the numbers:
24 / 10 = 2.4
120 / 18 = 6.666...
These ratios don't seem related.
Let's try to express the second number as a function of the first:
24 = f(10)
120 = f(18)
If we consider f(x) = x * (x/4 + some constant)
10 * (10/4 + c) = 24 => 25 + 10c = 24 => 10c = -1 => c = -0.1
18 * (18/4 + c) = 120 => 81 + 18c = 120 => 18c = 39 => c = 2.166...
This doesn't work.
Without a clear and consistent pattern, it's impossible to definitively determine the corresponding number for 13. The problem as stated is likely flawed, missing information, or relying on a complex pattern that is difficult to deduce with only two examples.
If we assume a simple linear relationship of the form y = ax + b, we have two equations:
24 = 10a + b
120 = 18a + b
Subtracting the first from the second:
96 = 8a
a = 12
Substituting back into the first equation:
24 = 120 + b
b = -96
So y = 12x - 96
If x = 13, then y = 12 * 13 - 96 = 156 - 96 = 60
So, if we assume a linear relationship, 13 would correspond to 60. However, without more information, this is just one possibility.
Final Answer: The final answer is 60?
Chat GPT said:
To find the relationship between the numbers, let's analyze the pattern.
1. **First pair: \(10 \to 24\)**
- A possible operation: \(10 \times 2 + 4 = 24\).
2. **Second pair: \(18 \to 120\)**
- A similar operation might apply: \(18 \times 6 + 12 = 120\).
Let’s determine a rule:
- Multiply the first number by a factor, then add a number.
- The factor and addition might depend on the input.
Let’s check if this reasoning applies consistently.
---
- For \(10 \to 24\), the factor is \(2.4\) (\(24/10\)).
- For \(18 \to 120\), Factor Logical ** Apply
Let's identify a clear pattern:
1. For \( 10 \to 24 \):
\( 10 \times 2 + 4 = 24 \).
2. For \( 18 \to 120 \):
\( 18 \times 6 + 12 = 120 \).
The multiplication factor increases with the input, and the addition follows a pattern. Let’s analyze this systematically.
---
- \( 10 \to 2 \),
- \( 18 \to 6 \).
**Assumption**: The multiplier might grow linearly with the input.
2. The addition term:
- \( 4 \) for \( 10 \),
- \( 12 \) for \( 18 \).
This also increases.
---
For \( 13 \):
1. Interpolating the multiplier:
- \( 10 \to 2 \),
- \( 18 \to 6 \).
Slope = \( \frac{6 - 2}{18 - 10} = \frac{4}{8} = 0.5 \).
At \( 13 \): \( 2 + (13 - 10) \times 0.5 = 2 + 1.5 = 3.5 \).
Multiplier = \( 3.5 \).
2. Interpolating the addition:
- \( 4 \) for \( 10 \),
- \( 12 \) for \( 18 \).
Slope = \( \frac{12 - 4}{18 - 10} = 1 \).
At \( 13 \): \( 4 + (13 - 10) \times 1 = 4 + 3 = 7 \).
Addition = \( 7 \).
---
1. **First pair: \(10 \to 24\)**
- A possible operation: \(10 \times 2 + 4 = 24\).
2. **Second pair: \(18 \to 120\)**
- A similar operation might apply: \(18 \times 6 + 12 = 120\).
Let’s determine a rule:
- Multiply the first number by a factor, then add a number.
- The factor and addition might depend on the input.
Let’s check if this reasoning applies consistently.
---
- # Testing the Rule for \(13 \to ?\):
- For \(10 \to 24\), the factor is \(2.4\) (\(24/10\)).
- For \(18 \to 120\), Factor Logical ** Apply
Let's identify a clear pattern:
1. For \( 10 \to 24 \):
\( 10 \times 2 + 4 = 24 \).
2. For \( 18 \to 120 \):
\( 18 \times 6 + 12 = 120 \).
The multiplication factor increases with the input, and the addition follows a pattern. Let’s analyze this systematically.
---
- # Step-by-Step:
- \( 10 \to 2 \),
- \( 18 \to 6 \).
**Assumption**: The multiplier might grow linearly with the input.
2. The addition term:
- \( 4 \) for \( 10 \),
- \( 12 \) for \( 18 \).
This also increases.
---
For \( 13 \):
1. Interpolating the multiplier:
- \( 10 \to 2 \),
- \( 18 \to 6 \).
Slope = \( \frac{6 - 2}{18 - 10} = \frac{4}{8} = 0.5 \).
At \( 13 \): \( 2 + (13 - 10) \times 0.5 = 2 + 1.5 = 3.5 \).
Multiplier = \( 3.5 \).
2. Interpolating the addition:
- \( 4 \) for \( 10 \),
- \( 12 \) for \( 18 \).
Slope = \( \frac{12 - 4}{18 - 10} = 1 \).
At \( 13 \): \( 4 + (13 - 10) \times 1 = 4 + 3 = 7 \).
Addition = \( 7 \).
---
- # Final Calculation:
- # Answer:
g4ry13 said:
There were more calculations, but good old PH barfed on the post, so I had to summarise.
GPT said:
To determine mm and nn for 1313, observe that mm and nn increase with xx. Let's interpolate their values:
Interpolating mm and nn for 1313:
Using a linear relationship:
m=2+6?218?10?(13?10)=2+48?3=2+1.5=3.5
m=2+18?106?2??(13?10)=2+84??3=2+1.5=3.5
n=4+12?418?10?(13?10)=4+88?3=4+3=7
n=4+18?1012?4??(13?10)=4+88??3=4+3=7
Calculate for 1313:
13?(13×3.5)+7=45.5+7=52.5
13?(13×3.5)+7=45.5+7=52.5
Since 52.5 is not an option, we round to the nearest value, which is 50.
Final Answer:
50
EDIT: here's a screenshot of the calcs.Interpolating mm and nn for 1313:
Using a linear relationship:
m=2+6?218?10?(13?10)=2+48?3=2+1.5=3.5
m=2+18?106?2??(13?10)=2+84??3=2+1.5=3.5
n=4+12?418?10?(13?10)=4+88?3=4+3=7
n=4+18?1012?4??(13?10)=4+88??3=4+3=7
Calculate for 1313:
13?(13×3.5)+7=45.5+7=52.5
13?(13×3.5)+7=45.5+7=52.5
Since 52.5 is not an option, we round to the nearest value, which is 50.
Final Answer:
50
Edited by TonyRPH on Friday 27th December 18:37
essayer said:
(n-8) * 12
so 13 is to (5*12) = 60
If you graph the data points you have, there are an infinite number of curves which are 'solutions', so the third point can be anything you like.so 13 is to (5*12) = 60
Edited by essayer on Friday 27th December 18:18
But the simplest solution is a straight line.
If you've got 3 arbitrary data points, the simplest solution might involve x^2 terms.
There are unlimited possibilities, the 'answer' might be anything from ASCII character values in a string of text through to car registrations.
It reeks of either a question set by a 'teacher' with a poor grasp of fundamental maths, or the question being munged between being asked and the OP getting hold of it.
Radec said:
That question is for an 11 year old?
Looks like the final question you'd get on the 1% Club gameshow.
Think im going to be in trouble when my lad grows up and needs help with his homework lol.
You are not wrong. My daughter is 13…her maths homework is on a website, there is a video if you are struggling to explain it…I get ‘her’ to watch that so I can see it and then explain it to her!Looks like the final question you'd get on the 1% Club gameshow.
Think im going to be in trouble when my lad grows up and needs help with his homework lol.
OutInTheShed said:
If you graph the data points you have, there are an infinite number of curves which are 'solutions', so the third point can be anything you like.
But the simplest solution is a straight line.
If you've got 3 arbitrary data points, the simplest solution might involve x^2 terms.
There are unlimited possibilities, the 'answer' might be anything from ASCII character values in a string of text through to car registrations.
It reeks of either a question set by a 'teacher' with a poor grasp of fundamental maths, or the question being munged between being asked and the OP getting hold of it.
Indeed. If the relationship was a quadratic of formula y = ax^2 + bx + c, then you can get any answer n using a = 4 - n/15, b = 28n/15 - 100, and c = 624 - 12n.But the simplest solution is a straight line.
If you've got 3 arbitrary data points, the simplest solution might involve x^2 terms.
There are unlimited possibilities, the 'answer' might be anything from ASCII character values in a string of text through to car registrations.
It reeks of either a question set by a 'teacher' with a poor grasp of fundamental maths, or the question being munged between being asked and the OP getting hold of it.
If the relationship was y = 1 / (13 - x) + 181/15 x - 97, there is no solution when x = 13.
Perhaps the teacher posed a question that AI would find difficult to answer.
This is the thinking of my 73-year old brain that has been retired from work for 20-years. It is about number of characters and number progression.
TWENTY FOUR = 10(c) – 0 = 10
ONE HUNDRED AND TWENTY = 19(c) – 1 = 18
THIRTEEN = 8(c) -2 = 6
AI never tries to think outside the box, it “knows what it knows” and can think quickly - so it can be taught to look out for tricks like this in the future.
This is the thinking of my 73-year old brain that has been retired from work for 20-years. It is about number of characters and number progression.
TWENTY FOUR = 10(c) – 0 = 10
ONE HUNDRED AND TWENTY = 19(c) – 1 = 18
THIRTEEN = 8(c) -2 = 6
AI never tries to think outside the box, it “knows what it knows” and can think quickly - so it can be taught to look out for tricks like this in the future.
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