Daily Math Puzzle: 2026-10-05

Use the Rune of Mighty Blow twice. — Let's break down the probability of success for each strategy: **Rune of Swift Strike (S):** P(10 damage) = 1/2, P(0 damage) = 1/2 **Rune of Mighty Blow (M):** P(15 damage) = 1/3, P(0 damage) = 2/3 The goal is to deal AT LEAST 12 damage. **Option 1: Use the Rune of Swift Strike twice.** Possible outcomes and their probabilities: - 10 + 10 = 20 damage: (1/2) * (1/2) = 1/4 - 10 + 0 = 10 damage: (1/2) * (1/2) = 1/4 - 0 + 10 = 10 damage: (1/2) * (1/2) = 1/4 - 0 + 0 = 0 damage: (1/2) * (1/2) = 1/4 Only the 20 damage outcome is sufficient (>= 12 damage). Probability of victory = 1/4 = 0.25 **Option 2: Use the Rune of Mighty Blow twice.** Possible outcomes and their probabilities: - 15 + 15 = 30 damage: (1/3) * (1/3) = 1/9 - 15 + 0 = 15 damage: (1/3) * (2/3) = 2/9 - 0 + 15 = 15 damage: (2/3) * (1/3) = 2/9 - 0 + 0 = 0 damage: (2/3) * (2/3) = 4/9 Outcomes sufficient for victory (>= 12 damage): 30 damage, 15 damage (from both combinations). Probability of victory = P(30 damage) + P(15 damage from 1st hit) + P(15 damage from 2nd hit) = 1/9 + 2/9 + 2/9 = 5/9 ≈ 0.556 **Option 3: Use the Rune of Swift Strike once, then the Rune of Mighty Blow once.** Possible outcomes and their probabilities (order doesn't affect total damage): - S=10, M=15 => Total 25 damage: (1/2) * (1/3) = 1/6 - S=10, M=0 => Total 10 damage: (1/2) * (2/3) = 2/6 - S=0, M=15 => Total 15 damage: (1/2) * (1/3) = 1/6 - S=0, M=0 => Total 0 damage: (1/2) * (2/3) = 2/6 Outcomes sufficient for victory (>= 12 damage): 25 damage, 15 damage. Probability of victory = P(S=10, M=15) + P(S=0, M=15) = 1/6 + 1/6 = 2/6 = 1/3 ≈ 0.333 **Comparison:** - Option 1 (Swift Strike twice): 0.25 - Option 2 (Mighty Blow twice): ≈ 0.556 - Option 3 (Swift Strike once, Mighty Blow once): ≈ 0.333 The highest probability of victory comes from using the Rune of Mighty Blow twice (5/9). This is a tricky problem because both runes have the same average damage per use (Swift Strike: (10*1/2)+(0*1/2)=5; Mighty Blow: (15*1/3)+(0*2/3)=5). However, when considering a specific threshold like 12 damage, the higher potential damage from the Mighty Blow rune, even with its lower individual success rate, makes it more likely to cumulatively exceed the threshold.