1. **State the problem:** Create a 1-page cheat sheet with formulas only, covering starred concepts from the notes and user text. 2. **Identify starred concepts:** Arithmetic sequences, sums of sequences, digital roots, modular arithmetic, magic squares, rebus puzzles, Sudoku logic, and clock problems. 3. **Formulas and key concepts:** - Arithmetic sequence nth term: $$a_n = a_1 + (n-1)d$$ - Sum of arithmetic sequence: $$S_n = \frac{n}{2}(a_1 + a_n)$$ - Sum of first n odd numbers: $$1 + 3 + 5 + \cdots + (2n-1) = n^2$$ - Digital root: Sum digits repeatedly until one digit remains. - Modular arithmetic: $$a \equiv b \pmod{m}$$ means $$m | (a-b)$$ - Magic square (3x3) sum: $$\text{Magic sum} = \frac{n(n^2+1)}{2}$$ for numbers 1 to $$n^2$$ - Clock arithmetic: Hours mod 12 or 24 depending on context. - Sudoku rules: Each row, column, and 3x3 box contains unique digits/letters. - Rebus puzzles: Use letter/word manipulation logic. 4. **Additional notes:** - Percentage markdown formula: $$\text{New Price} = \text{Original Price} \times (1 - r)^k$$ where $$r$$ is markdown rate, $$k$$ number of markdowns. - Digital root multiplication property: $$\text{DR}(a \times b) = \text{DR}(\text{DR}(a) \times \text{DR}(b))$$ 5. **Summary:** This cheat sheet compiles essential formulas and rules for arithmetic sequences, sums, digital roots, modular arithmetic, magic squares, Sudoku, rebus puzzles, and clock problems, enabling quick reference during tests.