The difference between 3.5 and 4 is substantial. Here is what 4 says
To find the number of combinations in which four friends (A, B, C, and D) can stand in line such that A and C are not next to each other, we can use the following approach:
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Total Combinations: First, calculate the total number of ways in which four people can be arranged in a line. This can be calculated by (4!) (4 factorial), since there are 4 slots to fill, each choice reducing the number of available choices by one for the next slot. [ 4! = 4 \times 3 \times 2 \times 1 = 24 ]
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Unwanted Combinations (Where A and C are next to each other):
- Consider A and C as a single unit. This effectively reduces the number of units to arrange from 4 to 3 (the AC unit, B, and D).
- These three units can be arranged in (3!) ways: [ 3! = 3 \times 2 \times 1 = 6 ]
- However, within the AC unit, A and C can switch places. So, there are 2 ways to arrange A and C within their unit.
- Therefore, the total number of arrangements where A and C are next to each other is: [ 3! \times 2 = 6 \times 2 = 12 ]
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Subtracting Unwanted Combinations: Subtract the number of unwanted combinations (where A and C are next to each other) from the total number of combinations: [ 24 - 12 = 12 ]
Thus, there are 12 combinations where A and C are not next to each other.
I hear you. You make very good points.
I'm tempted to argue that many humans aren't generally intelligent based on your definition of requiring original thought/solving things they haven't been told/trained on, but we don't have to go there. Lol
Can you expand on your last paragraph? You're saying if the model was trained on more theory and less examples of solved problems it might be improved?