Daily Math Puzzle: 2026-10-08
Sharpen your mathematical thinking with fresh puzzles delivered daily.
🧩 New Puzzle Every Day — Free
2026-10-08
During a 'mind-reading' act, a magician secretly places an unknown number of coins under an upside-down cup. They then ask a volunteer to follow these steps precisely: 1. Think of any positive whole number. 2. Add this number to the count of coins under the cup. 3. Multiply the new total by 2. 4. Subtract 4 from the result. 5. Divide this new total by 2. 6. Finally, subtract the original number you thought of. The volunteer states their final result aloud. The magician, without ever knowing the volunteer's original chosen number, immediately declares the exact number of coins under the cup. If a volunteer's final result was 19, how many coins were originally under the cup?
🔥 Build your streak — solve daily in the app
Solution
21 — Let 'C' represent the unknown number of coins under the cup, and 'X' be the positive whole number the volunteer thought of.
Let's follow the steps algebraically:
1. Volunteer thinks of X.
2. Add X to C: C + X
3. Multiply by 2: 2 * (C + X) = 2C + 2X
4. Subtract 4: 2C + 2X - 4
5. Divide by 2: (2C + 2X - 4) / 2 = C + X - 2
6. Subtract the original number X: (C + X - 2) - X = C - 2
The final result the volunteer gives is always 'C - 2', regardless of the initial number 'X' they chose (as 'X' cancels out).
Since the volunteer's final result was 19, we can set up the equation:
C - 2 = 19
To find C, add 2 to both sides of the equation:
C = 19 + 2
C = 21
Therefore, there were 21 coins originally under the cup.
Never Miss a Daily Puzzle
Download TestPrepMagic and get push notifications for each day's puzzle. Build daily streaks and track your improvement.
Download Free AppRelated Puzzles
Math Puzzle: 2026-10-07
A cutting-edge tech startup, 'TrendSense', developed an AI that predicts stock market fluctuations with near-perfect accuracy by analyzing real-time global news feeds. Its CEO, Alex, secured a crucial pitch with a major venture capitalist, 'PeakCapital', known for its offices on the top floor of a skyscraper. Alex, confident in his live demo on his tablet, rode the elevator alone to the 50th floor, delivered an impressive pitch, and left feeling optimistic. The next day, PeakCapital rejected their funding, stating, 'Your core technology is fundamentally flawed. We tested it, and it failed consistently.' Alex was stunned; his AI had never failed a test. What non-obvious environmental factor most likely caused the AI's failure during PeakCapital's test?
Math Puzzle: 2026-10-06
During a school field trip to a historic courthouse, the judge challenged the students with a word puzzle. He said, 'I am a six-letter word that represents what we strive for here: fair and ethical treatment. Interestingly, I contain the letters 'I', 'V', and 'E', but I do not contain the letter 'S' at all. What word am I?'
Math Puzzle: 2026-10-05
A valiant adventurer stands before the fearsome Goblin King, who has only 12 health points remaining. To defeat him, the adventurer must deal at least 12 points of damage. The King offers a choice of two ancient magical runes:
1. **Rune of Swift Strike:** Has a 1/2 chance to deal 10 damage and a 1/2 chance to deal 0 damage on each use.
2. **Rune of Mighty Blow:** Has a 1/3 chance to deal 15 damage and a 2/3 chance to deal 0 damage on each use.
The adventurer has time to use runes twice. Which strategy offers the highest probability of defeating the Goblin King?