Here's another one. The part that LLMs
Here's another one. The part that LLMs appear not to get is the number of blocks and the final dimensions:
The following shapes are composed of equal sized cubes glued together such that the dimensions are 3 cubes by 4 cubes and one cube deep. 1) A “U” shape, and 2) A “T” shape. How might a solid shape with no internal gaps be created without unglueing any of the blocks? How many blocks are in the final shape? What is the name of the shape? What are the dimensions of the shape?
2 Replies
5 high 3 wide if you just insert the t inside the u its a rectangle
(had to read it 3 times tho :D)
yes, exactly
Here's one where the models almost always try to factor the sum of the volumes into 3 integers, which will lead to erroneous results, rather than by considering the shapes of the pieces (almost all of them try to use the wrong combination below, and most miss one or two of the correct ones as well):
I have four shapes made by gluing together identical smaller cubes. One shape is a box of dimensions 3 x 3 x 4 cubes. It is made out of only 32 cubes. The three remaining shapes are solid rectoids of size 3 x 3 x 1 cubes, 1 x 1 x 4 cubes, and 3 x 4 x 1 cubes. Which shapes can be fitted together to form other solid rectoids different from the ones that already exist. You are not allowed to break apart any of the shapes that are already glued together.
Solution:
A = 3x3x4, B=3x3x1, C=1x1x4, D=3x4x1
A+ C (3x3x4)
A+B+C (3x3x5)
A+B+D(3x4x4)
C+D (4x4x1)
B+C (7x3x1)
Wrong:
B+C+D (they try to pass it off as 5x5x1)
This may be a useful question because different LLMs seem score over a wide continuum. I would consider this question "spacial" reasoning, and it may be a type that we can use to differentiate models.
This one is kind of interesting:
A runner is jogging at a rate of one meter per second on a treadmill and is exactly centered. A drop of sweat falls from his chin and contacts the treadmill exactly 0.8 meters from the front of the treadmill. How long will it take for the bead of sweat to make it to the front of the treadmill? For the purposes of this question, assume that the bead of sweat does not smear or migrate on the treadmill belt once it makes contact, it simply sticks in place.
Solution: 2.4 seconds (travels backward for 0.8s, then forward for 1.6s).
Every LLM I've tried either says 0.8s or it never reaches the front. None of them seem to understand that the belt travels around such that the bead of sweat will travel toward the front of the treadmill underneath after first moving away from the runner.