Analogical Prompting: let the model write its own examples

Ask a model a tricky problem cold and it does what it always does — grabs the nearest familiar pattern and runs with it. On problems that have a well-known trap, the nearest pattern is exactly the wrong one. Try this one: how many 3-digit numbers have all distinct digits? The clean, tempting answer is 10 × 9 × 8 = 720. It's wrong. The first digit can't be 0 (or you're counting things like 072, which isn't a 3-digit number), so it's 9 × 9 × 8 = 648. A model answering from a cold start reaches…