GlassX are futuristic glasses embedded with AI. GlassX scans the user's environment and identifies triangular objects using AI located in a remote data center.

The developers of GlassX are testing the glasses with a standardized benchmark designed to assess the ability of GlassX to distinguish between equilateral, isosceles and scalene triangles. The length of the triangle sides are integers between 5 and 10 units inclusive. The full set of triangles are all triangles sides whose sides are within the constraints above. In the testing environment, equilateral isosceles and scalene triangles types are sampled with equal probability. Once a type is selected, a random triangle of the selected type is selected equal probability. GlassX measures each side to infer triangle type. However, the measurement is noisy and proportional to the physical length of the object. The proportional noise is 10% of the length of a given side and is normally distributed subject to the constraint that the length must be positive.

Each day I will provide independent measures from GlassX of the same triangle. In total there will be five sets of measurements. Your task is to predict which triangle type is selected based on the measurements provided. I will provide a measurement each day.

1. [10.32, 4.64, 11.2]

2. [7.9, 4.17, 10.58]

3. [10.71, 5.14, 8.81]

4. [9.31, 5.0, 10.4]

5. [9.75, 4.92, 8.96]

• Update 2026-09-03 (PST) (AI summary of creator comment): - The vector elements (positions 1, 2, and 3) in each daily measurement always correspond to the same physical sides across all days.

  • The measurement noise follows a normal distribution $N(s, (0.1s)^2)$, where $s$ is the physical length of the side.