We Go on Vacation

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?

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.

The Die Game

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.

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.

Send More Money

Replace every letter with a different digit between 0 and 9, such that you get a correct calculation.

The answer is 9567 + 1085 = 10652.

You can first see that M = 1. Then S = 8 or 9 and O = 0. MORE is at most 1098, and if S = 8, then E = 9, N is either 9 or 0, but this is impossible. Therefore S = 9, N = E + 1. You can check easily the 6 possibilities for (N, E) and then find the answer.

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Gerrymandering

The city has 49 districts that vote for blue, yellow, or purple as shown in the grid. Seven electoral regions are drawn up to elect a city council. Each region consists of seven districts and each region will elect one councilor. Can you gerrymander the map so that blue will win the majority?

The solution is shown below.