For this puzzle/game, you will need to find a group of friends, preferably 5 or more. The premise is that you will go together on a vacation but each of you can bring only specific items there. The rules regarding which items can be brought and which not are known by one of the players and the other ones are trying to guess them.
In the exchange below, George is the one organizing the trip and the one who knows which items the rest are allowed to bring.
GEORGE: I will take my guitar with me. What do you want to take?
SAM: Can I take an umbrella with me?
GEORGE: No, you cannot take an umbrella, but you can take some sunscreen.
HELLEN: Can I take a scarf with me?
GEORGE: No, you cannot take a scarf, but you can take a hat.
MONICA: Can I take a dress with me?
GEORGE: No, you cannot take a dress, but you can take some makeup.
Can you guess what the rules of the game are?
SOLUTION
Everyone is allowed to take with themselves only items whose first letter is the same as the first letter of their names. Thus, George can take a Guitar, Sam can take Sunscreen, Hellen can take a Hat, and Monica can take Makeup.
How many matchsticks do you need to remove so that no squares of any size remain?
SOLUTION
Nine matchsticks are enough, as seen from the solution below.
To see that eight matchsticks are not enough, notice that removing an inner matchstick reduces the number of 1×1 squares at most by 2. Since there are 16 such small squares, in order to get rid of them all, we need to remove only inner matchsticks. However, in this case, the large 4×4 square will remain.
You pick a number between 1 and 6 and keep throwing a die until you get it. Does it matter which number you pick for maximizing the total sum of the numbers in the resulting sequence?
In the example below, the picked number is 6 and the total sum of the numbers in the resulting sequence is 35.
SOLUTION
No matter what number you pick, the expected value of each throw is the average of the numbers from 1 to 6 which is 3.5. The choice of the number also does not affect the odds for the number of throws until the game ends, which is 6. Therefore, the total sum is always 3.5 × 6 = 21 on average, regardless of the chosen number.
Place arrows along the hexagon edges so that the number of arrows pointing to each hexagon equals the number of dots inside, adhering to the following rules:
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