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
