📘 logic and algebra

1. The problem presents a pattern in the sums: 1 + 4 = 5, 2 + 5 = 12, 3 + 6 = 21, and asks for 8 + 11 = ? 2. At first glance, the sums don't follow normal addition rules, so we loo

1. **Problem Statement:** We have 5 keys and 5 locks. Each key has a number of engraved lines, and each lock requires a key with specific characteristics based on the number of eng

1. The first problem is to find if there exists an integer $x$ such that $$2x^2 - 4 = 0.$$ 2. Start by solving the equation:

1. **Problem:** Find the pattern and determine the output for 9 given:\n4 → 13, 7 → 22, 1 → 4, 9 → ?\n**Step 1:** Look for a formula relating input $x$ to output $y$.\nCheck if $y

1. Complete the sequence described with 3x3 grids and patterns. Without specific visuals or pattern descriptions, this part cannot be solved precisely from the text alone.