Comment by gloosx
1 year ago
Just leaving here an example of the "smart chain of thought", which took the model about 20s of thinking. The problem I asked was – "what 3 numbers give the same result when divided and added together". Seems the current state of art is that basic school problems are too hard yet even for this new chain-of-marketing.
Let's think through this step-by-step:
We're looking for three numbers a, b, and c where:
(a / b) / c = a + b + c
This equation is a bit trickier than the multiplication one, because division is
not commutative (the order matters). We need to be careful about how we
interpret (a / b) / c.
Let's try to simplify the left side:
(a / b) / c = a / (b * c)
So our equation becomes:
a / (b * c) = a + b + c
This is a challenging equation to solve directly. Let's try some numbers:
If we use 1, 2, 3 like before:
1 / (2 * 3) = 1/6 ≠ 1 + 2 + 3 = 6
Let's try smaller numbers, like fractions:
1/2, 1/3, 1/6
Let's check:
(1/2 / 1/3) / 1/6 = (1/2 * 3) / 1/6 = 3/2 * 6 = 9
1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1
This doesn't work either. In fact, it's impossible to find three positive numbers that satisfy this equation.
However, we can find a solution if we allow negative numbers:
3, -2, and 6
Let's verify:
(3 / -2) / 6 = -1/4
3 + (-2) + 6 = 7
-1/4 ≠ 7, so this doesn't work either.
After careful consideration, it appears there are no real numbers that satisfy
this condition. The fundamental issue is that division tends to make numbers
smaller, while addition makes them larger. It's mathematically impossible to
find three numbers where these operations result in the same value.
nuff said
what does divided together mean? maybe your question doesn't have a good answer, because the question is not formulated well enough.
That's a classical school question, word-by-word, except multiplication is replaced by division
With multiplication the question makes sense due to the commutative property but division does not have that so the question becomes ambiguous... And now I see that the model even points this out.
5 replies →
Order doesn't matter with multiplication (eg: (20 * 5) * 2 == (5 * 2) * 20) but it obviously does with division ((20/5)/2 != (2/5)/20) so the question doesn't make sense. It's you making grade-school level mistakes here.
4 replies →
{0, -1, 1}. Divide (in order): 0/-1 -> 0/1 -> 0. Add: 0 - 1 + 1 = 0
also {-1, 1, 1}
Seems not to work as division yields -1 (-1/1/1) and adding them yields +1 (-1+1+1).
Claude 3.5 seems to get it, (thought the method is not what I would use?) -
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Let's think through this step-by-step:
————
Certainly, let's approach this problem step-by-step:
1) First, let's write out our equation: (a / b) / c = a + b + c
2) To simplify the left side, we can rewrite it as: a / (b * c) = a + b + c
3) Now, to solve this, we need to find values for a, b, and c that satisfy this equation. Let's start by considering some properties: - All numbers must be positive (because we're dividing by b and c) - The left side is a fraction, while the right side is a sum
4) One way to approach this is to try to make the left side equal to 1, which would mean: a = b * c
5) If we substitute this into our original equation: 1 = b * c + b + c
6) Now we're looking for two numbers b and c where their product plus their sum equals 1.
7) Let's try some small numbers: If b = 1/2 and c = 1/2: (1/2 * 1/2) + 1/2 + 1/2 = 1/4 + 1 = 5/4 ≠ 1
8) Let's try smaller numbers: If b = 1/3 and c = 1/3: (1/3 * 1/3) + 1/3 + 1/3 = 1/9 + 2/3 = 7/9 ≠ 1
9) Even smaller: If b = 1/4 and c = 1/4: (1/4 * 1/4) + 1/4 + 1/4 = 1/16 + 1/2 = 9/16 ≠ 1
10) We're getting closer. Let's try b = 1/4 and c = 1/3: (1/4 * 1/3) + 1/4 + 1/3 = 1/12 + 1/4 + 1/3 = 1/12 + 3/12 + 4/12 = 8/12 = 2/3 ≠ 1
11) Let's adjust further. If b = 1/3 and c = 1/4: (1/3 * 1/4) + 1/3 + 1/4 = 1/12 + 1/3 + 1/4 = 1/12 + 4/12 + 3/12 = 8/12 = 2/3 ≠ 1
12) One more try. Let's use b = 1/2 and c = 1/3: (1/2 * 1/3) + 1/2 + 1/3 = 1/6 + 1/2 + 1/3 = 1/6 + 3/6 + 2/6 = 6/6 = 1
13) We found it! When b = 1/2 and c = 1/3, the equation holds.
14) Remember, we set a = b * c, so a = 1/2 * 1/3 = 1/6
Therefore, one solution to the equation (a / b) / c = a + b + c is: a = 1/6, b = 1/2, and c = 1/3
We can verify: (1/6 / 1/2) / 1/3 = (1/3) / 1/3 = 1 1/6 + 1/2 + 1/3 = 1/6 + 3/6 + 2/6 = 1
This solution satisfies the equation.
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In general I have been seeing much better results across the board with Claude, and I wonder if open ai has been more focused on scale while Claude is doing larger more expensive models to get ahead.
It's crazy that it just tries to bruteforce it by picking numbers, and in your case it took more steps before concluding a success/failure, which seems quite to be random to me, or at least dependent on something.
What's clear is that it doesn't have any idea about mathematical deduction and induction – a real chain-of-thought which kids learn in 5th grade.
Lots of people don’t either. I think it probably just needs more 5th grade math problems in the rlhf corpus :)
1 reply →
(0/-1)/1=0
0+(-1)+1=0