This tutorial explores TileGym GPU programming by building a Colab workflow that runs across different hardware conditions. It begins by probing the CUDA environment, checking whether NVIDIA cuTile runs directly, and falling back to Triton when standard Colab GPUs lack the required cuTile stack. The core tile-programming idea is that instead of writing code for one thread at a time, users operate on entire data tiles, load them into the kernel, compute on them efficiently, and store results back. The model is used to implement vector addition, fused GELU, row-wise softmax, tiled matrix multiplication, and flash attention, comparing each result against PyTorch for correctness and benchmarking. The environment probe checks for CUDA availability, compute capability, and Torch CUDA runtime. Real cuTile installation is attempted only if compute capability is >= 8.0 and CUDA major version is >= 13; otherwise, the tutorial falls back to Triton, which teaches the same tile-based programming model.