Daily Math Puzzle: 2026-07-14

81% — Let's assume the magician starts with 100 cards for easy calculation. If you use a variable, the percentage will be the same. **Step 1: 25% of the cards vanish.** Initial cards: 100 Cards vanished: 25% of 100 = 0.25 * 100 = 25 cards. Cards remaining after Step 1: 100 - 25 = 75 cards. **Step 2: From the cards remaining (75 cards), he magically duplicates 20% of them.** Amount duplicated: 20% of 75 = 0.20 * 75 = 15 cards. New total number of cards: 75 + 15 = 90 cards. **Step 3: He gives away 10% of the *current total* (90 cards) to his assistant.** Amount given away: 10% of 90 = 0.10 * 90 = 9 cards. Final number of cards in the stack: 90 - 9 = 81 cards. Since we started with 100 cards and ended with 81 cards, the percentage of the original number of cards remaining is 81%. **Common pitfalls avoided by this method:** * **Applying all percentages to the original base:** Simply adding/subtracting percentage points (e.g., 100 - 25 + 20 - 10 = 85) incorrectly assumes all percentages are based on the initial total, rather than the changing current total. * **Prematurely stopping:** Ending the calculation after Step 2 would give 90%. * **Misinterpreting 'duplicates' as 'removes':** If 'duplicates 20%' was mistaken for 'removes 20%', the calculation would be 100 * (1 - 0.25) * (1 - 0.20) * (1 - 0.10) = 100 * 0.75 * 0.80 * 0.90 = 54.