Trefoil Puzzle #166: Airplane seats

People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can’t remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it’s available, otherwise they will choose an open seat at random to sit in.

The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?

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Answers to Newsletter Puzzles

We hope you enjoyed solving the festive puzzles published in our December newsletter!

As promised, here are the answers:

1. 12 Days Of Christmas
According to the traditional song, on the first day of Christmas, my true love sent me a partridge in a pear tree. On the second day of Christmas, my true love sent me three presents: two turtle doves and a partridge in a pear tree. On the third day of Christmas, my true love gave me six presents: three French hens, two turtle doves and a partridge in a pear tree. This carries on until the twelfth day of Christmas. After the twelve days of Christmas are over, how many presents has my true love sent me altogether? Is there a quick way to work out the answer?

Click the post to read the answers!


Trefoil Puzzle #165

By using the numbers 8, 5, 3 and 1 exactly once each, and with the help of brackets and basic operations (adding, subtracting, multiplying and dividing), can you form an expression with a value of 20?


Trefoil Puzzle #164

he owner of a banana plantation has a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 km. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.

What is the largest number of bananas you can bring over to your destination?


Trefoil Puzzle #163

You are blindfolded and 10 coins are place in front of you on table.

You are allowed to touch the coins, but can’t tell which way up they are by feel. You are told that there are 5 coins head up, and 5 coins tails up but not which ones are which.

How do you make two piles of coins each with the same number of heads up?


Trefoil Puzzle #161

You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more.
How can you find the ball that is heavier by using a balance and only two weighings?


Trefoil Puzzle #160

You have two ropes and a lighter. Each rope has the following property: If you light one end of the rope, it will take one hour to burn to the other end. They don’t necessarily burn at a uniform rate. How can you measure a period of 45 minutes?