# brain-teaser

# How to Solve These 5 Brain-Teasers in 10 Minutes or Less

Brain-teasers are puzzles that challenge your logical thinking, creativity and problem-solving skills. They can be fun and stimulating, but also frustrating and time-consuming. Here are some tips on how to solve five common brain-teasers in 10 minutes or less.

**The Missing Dollar**: Three friends go to a hotel and rent a room for $30. They each pay $10 and go to their room. The manager realizes that he overcharged them by $5 and sends the bellboy to return the money. The bellboy decides to keep $2 for himself and gives $1 to each friend. So each friend paid $9, and the bellboy has $2. That makes $27. Where is the missing dollar?**The Monty Hall Problem**: You are on a game show where you have to choose one of three doors. Behind one door is a car, and behind the other two are goats. You pick a door, say Door 1, and the host, who knows what’s behind the doors, opens another door, say Door 3, which has a goat. He then asks you if you want to switch your choice to Door 2. Should you switch or stay?**The Two Fuses**: You have two fuses, each of which burns for exactly one hour. However, the fuses are not uniform, so they may burn faster or slower at different parts. You also have a lighter. How can you measure exactly 45 minutes using only these items?**The Three Light Bulbs**: You are in a room with three light switches, each of which controls one of three light bulbs in another room. You can only enter the other room once, and you cannot see or touch the light bulbs from the first room. How can you determine which switch controls which bulb?**The Four People and the Bridge**: Four people need to cross a bridge at night. They only have one flashlight, which they must share. The bridge can only hold two people at a time, and anyone crossing must either hold or be with someone holding the flashlight. The four people have different walking speeds: A takes 1 minute, B takes 2 minutes, C takes 5 minutes and D takes 10 minutes. When two people cross together, they walk at the speed of the slower person. What is the fastest way for all four people to cross the bridge?

*Solution*: There is no missing dollar. The friends paid $27 in total, of which $25 went to the manager and $2 went to the bellboy. The mistake is to add the $2 to the $27 instead of subtracting it.

*Solution*: You should switch. When you first pick a door, you have a 1/3 chance of getting the car. When the host opens a door with a goat, he eliminates one wrong choice, but he does not change the probability of your initial choice. So you still have a 1/3 chance of getting the car if you stay. However, by switching, you are effectively choosing between the two remaining doors, one of which has the car. So you have a 2/3 chance of getting the car if you switch.

*Solution*: Light both ends of one fuse and one end of the other fuse at the same time. The first fuse will burn out in 30 minutes, since it is burning from both ends. At this point, light the other end of the second fuse. The second fuse will burn out in 15 minutes, since it has already burned for 30 minutes from one end. Therefore, you have measured 45 minutes in total.

*Solution*: Turn on Switch 1 and Switch 2 and leave them on for a few minutes. Then turn off Switch 2 and enter the other room. The bulb that is on is controlled by Switch 1. The bulb that is off but warm is controlled by Switch 2. The bulb that is off and cold is controlled by Switch 3.

*Solution*: The fastest way is for A and B to cross first (2 minutes), then A to go back with the flashlight (1 minute), then C and D to cross (10 minutes), then B to go back with the flashlight (2 minutes