The Counterfeit Coin Riddle

Step-by-Step Solution

Step 1: First Weighing

  1. Divide the 12 coins into three groups:

    • Group A: 4 coins
    • Group B: 4 coins
    • Group C: 4 coins (set aside)
  2. Weigh Group A against Group B.

Possible Outcomes:
  • If the scale balances, the counterfeit coin is in Group C (the 4 coins not weighed).
  • If the scale tilts, the counterfeit coin is among the 8 coins on the scale, and we now know whether it is heavier or lighter.

Step 2: Second Weighing

  • Take three coins from the suspected group (either Group C if the first weighing balanced, or the tilting group if not).
  • Weigh them against three known good coins.
Possible Outcomes:
  1. If the scale balances, the counterfeit coin is the one left out.
    • Since we already know whether the fake is heavy or light from Step 1, we now have the answer.
  2. If the scale tilts, we now know the counterfeit is one of the three being weighed and whether it is heavier or lighter.

Step 3: Third Weighing

  • Take two of the remaining suspected coins and weigh them against each other.
Possible Outcomes:
  • If the scale balances, the fake coin is the one left out.
  • If the scale tilts, we know exactly which one is fake and whether it is heavier or lighter.

Final Answer:

👉 You can always find the counterfeit coin and determine if it’s heavier or lighter in exactly 3 weighings.

You have 12 coins, but one is counterfeit and is either heavier or lighter than the rest.
You also have a balance scale and can only use it three times.

How do you find the counterfeit coin and determine whether it is heavier or lighter?

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The Car Problem Riddle

A man drives one mile at 30 mph.
How fast must he drive the second mile to average 60 mph for the total two-mile trip?

👉 It’s impossible.

To average 60 mph over 2 miles, he must complete the trip in 2 minutes (since 2 miles ÷ 60 mph = 2 minutes).

  • The first mile at 30 mph takes 2 minutes.
  • That means there is NO TIME LEFT to complete the second mile.

Even if he drove infinitely fast, he still wouldn’t reach the required average speed.

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The Hidden Word Riddle

What comes once in a second, twice in a decade, but never in a century?

The letter “D”.

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The Running Mystery Riddle

A man is running away from home.

  • He turns left, runs straight, then turns left again.
  • After his second turn, he sees two masked men waiting for him.

What is he doing?

He is running around the bases in a game of baseball.

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The 10th Floor Elevator Riddle

A man lives on the 10th floor of an apartment building.
Every morning, he takes the elevator down to the ground floor to go to work.
However, when he comes home, he only takes the elevator up to the 7th floor and walks the rest of the way to the 10th floor.

Why does he do this?

The man is a small and can only reach the 7th-floor button in the elevator.

  • When going down, he can press the ground floor button easily.
  • When going up, he cannot reach the button for the 10th floor, so he takes the elevator as high as he can reach (7th floor) and then walks the rest of the way up.
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The Two Jars and Marbles Puzzle

A king gives you two jars and 100 marbles—50 white and 50 black. He will randomly select one jar, then pick one marble from it.

  • If the marble is white, you win freedom.
  • If the marble is black, you are executed.

How should you distribute the marbles to maximize your survival?

Put 1 white marble in one jar and the remaining 99 marbles (49 white + 50 black) in the other jar.


Explanation:

  • The king has a 50% chance of picking either jar.
  • If he picks Jar 1 (1 white marble)100% survival.
  • If he picks Jar 2 (49 white + 50 black) → You have a 49/99 ≈ 49.49% chance of survival.

Total Probability of Survival:

50% × 100% + 50% × 49.49% = 50% + 24.75% = 74.75%

This setup gives you a 74.75% chance of survival, the highest possible.

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5

The Bridge and Flashlight Puzzle

Four people need to cross a rickety bridge at night, but they must use a single flashlight to see where they’re going. The bridge can only hold two people at a time, and both must move at the speed of the slower person. The flashlight must always be carried across the bridge, meaning someone must bring it back for the next group.

Each person takes a different time to cross:

  • Person A: 1 minute
  • Person B: 2 minutes
  • Person C: 5 minutes
  • Person D: 10 minutes

How can all four people cross the bridge in just 17 minutes?

Steps to Cross in 17 Minutes:

  1. A & B cross first (2 minutes) → A carries the flashlight.
    • Now A & B are on the far side.
  2. A returns with the flashlight (1 minute) → Now only A is on the starting side.
  3. C & D cross together (10 minutes) → B holds the flashlight.
    • Now C & D are on the far side with B.
  4. B returns with the flashlight (2 minutes) → Now only B is on the starting side.
  5. A & B cross again (2 minutes) → Now everyone is on the far side.

Total Time:

2 + 1 + 10 + 2 + 2 = 17 minutes

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10

The Train and the Birds Puzzle

Two trains are 50 miles apart, traveling toward each other at 25 miles per hour each. A bird starts flying from the front of one train at 100 miles per hour, flying back and forth between the two trains until they collide. How far does the bird travel before the collision?

The bird travels 100 miles before the trains collide.

Explanation:

Instead of calculating each individual leg of the bird’s flight, let’s take a simpler approach using time.

  1. Time until collision:

    • The two trains are 50 miles apart, moving toward each other at 25 mph each.
    • Their combined closing speed is 25 mph + 25 mph = 50 mph.
    • Since they are 50 miles apart, they will collide in 1 hour (50 miles ÷ 50 mph = 1 hour).
  2. Distance traveled by the bird:

    • The bird flies at 100 mph for the entire 1 hour before the trains collide.
    • Since speed × time = distance, the bird travels: 100 mph×1 hour=100 miles.100 \text{ mph} \times 1 \text{ hour} = 100 \text{ miles}.
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The Fishing Trip Puzzle

Two fathers and two sons go fishing. Each catches one fish, but at the end of the trip, they have only three fish in total. How is this possible?

They are a grandfather, a father, and a son—three people total.

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