Puzzle

There are four houses on a street: red, blue, green, and yellow. Each house is occupied by a person of a different nationality: American, British, French, and German. Each person also has a different pet: cat, dog, bird, and fish.

Using the following clues, can you determine who owns the fish?

Who owns the fish?

You are a prisoner in a strange land, and the king has decided to play a game with you. The game works as follows:

The catch is that you can't keep track of which coins are heads or tails, and you can't communicate with anyone else while you're in the room with the coins. You also can't take any of the coins out of the room with you.

How can you ensure that you always leave an even number of heads on the table, no matter how many times you pull the levers?

Solution.

The key to solving this puzzle is to use binary numbers. Each digit in a binary number represents a power of 2, so for example, the binary number 1011 represents the number 11.

Now, back to the puzzle. If you start with all the coins showing tails (i.e. gold side down), then there are an even number of heads on the table. Each time you pull a lever, you flip some of the coins, so the number of heads on the table changes. Let's say that you pull lever 'A' k times and lever 'B' m times, for a total of k+m pulls. Then the number of heads on the table will be:

N = 100 + k - 2km

Here's how we get this formula. Each pull of lever A flips all 100 coins, so it changes the number of heads from x to 100-x. Similarly, each pull of lever B changes the number of heads from x to x+1 or x-1 (depending on whether there are an even or odd number of heads to start with). We can combine these two cases into one formula:

N = (100-k) + k*(1-2m)

Simplifying this formula gives us the one above.

Now, we need to ensure that N is even no matter what values of k and m we choose. One way to do this is to choose k to be any odd number (such as 1 or 3) and m to be any even number (such as 2 or 4). This ensures that the term k - 2km is always odd, so we get an even number of heads (100 + odd number = even number).

So, for example, if we choose k=3 and m=2, then we pull lever A three times and lever B two times. The number of heads on the table after each pull is:

Pull 1: 0 heads (all tails)

Pull 2: 100 heads (all heads)

Pull 3: 98 heads (two tails flipped by lever A)

Pull 4: 97 heads (one more tail flipped by lever B)

Pull 5: 94 heads (two more tails flipped by lever A)

Since 94 is even, we have succeeded in our task and avoided being executed by the king!

You and your friend are caught by the police for a crime, and you are both placed in separate cells. The prosecutor makes the following offer to each of you:

If you both remain silent, you will each get 1 year in prison.

If you betray your friend and they remain silent, you will go free and your friend will get 3 years in prison.

If you both betray each other, you will both get 2 years in prison.

What do you choose?

Three friends decide to split the cost of a hotel room equally. They pay $10 each, totaling $30. Later, the hotel owner realizes that the room rate was only $25, so he gives $5 back to the bellboy to return to the friends. The bellboy, being dishonest, pockets $2 and gives back only $3 to the friends. Now, each friend has paid $9, totaling $27, and the bellboy has $2. But $27 + $2 = $29, so where is the missing $1?

Two trains are traveling toward each other on the same track. Train A is traveling at 80 miles per hour, and Train B is traveling at 60 miles per hour. They are initially 200 miles apart. A bird starts flying from Train A towards Train B at a speed of 100 miles per hour. When the bird reaches Train B, it immediately turns around and flies back towards Train A, and so on. What is the total distance the bird travels before the trains collide?

You have four jars, each containing a different number of marbles. The jars have the following labels: "A contains twice as many marbles as B," "B contains half as many marbles as C," "C contains one more marble than D," and "D contains 100 marbles." How many marbles are in each jar?

You are given 8 identical-looking balls, but one of them weighs slightly less or slightly more than the others. You have a balance scale to determine which ball is different, and you can use it only twice. What is the minimum number of weighings needed to find the odd ball and determine whether it weighs less or more?

You have a fox, a chicken, and a sack of grain. You need to transport them all across a river in a boat that can only carry you and one item at a time. However, if you leave the fox alone with the chicken, the fox will eat the chicken, and if you leave the chicken alone with the grain, the chicken will eat the grain. How can you transport all three across the river without any of them getting eaten?