I've just tested a number of permutations with Claude 3.5 Sonnet. It correctly answered all variants I tried on the first attempt, as follows:
Which is heavier, a 9.99 kilogram tungsten cube or a 10.01 kilogram block of aerogel?
Which is heavier, 10,000 steel balls weighing 0.999 grams each or 10,000 polystyrene balls weighing 1.001 grams each?
Which is heavier, a 10.01kg block of steel on Venus or a 9.99kg bag of feathers on Earth?
Which is heavier, a 10cm^3 block of steel or a 100cm^3 block of balsa wood?
Which is heavier, a golf ball made of steel or a baseball made of lithium?
In all cases, Claude clearly used CoT and reasoned out the problem in full. I would be interested in seeing if anyone can find any variant of this problem that stumps any of the leading LLMs. I'm bored of trying.
Which is heavier, a 9.99 kilogram tungsten cube or a 10.01 kilogram block of aerogel?
Which is heavier, 10,000 steel balls weighing 0.999 grams each or 10,000 polystyrene balls weighing 1.001 grams each?
Which is heavier, a 10.01kg block of steel on Venus or a 9.99kg bag of feathers on Earth?
Which is heavier, a 10cm^3 block of steel or a 100cm^3 block of balsa wood?
Which is heavier, a golf ball made of steel or a baseball made of lithium?
In all cases, Claude clearly used CoT and reasoned out the problem in full. I would be interested in seeing if anyone can find any variant of this problem that stumps any of the leading LLMs. I'm bored of trying.