Some light brain exercises.
I know I am supposed to be studying, but my brain always wanders when I actually have to use it.
Some of the brainteasers that I came across, which I thought worthy to write down. Who knows, they may come in handy...
#1 Dwarves in a Cave
There are ten dwarfs in a dark cave. Inside the cave are ten dwarf hats - five red and five blue. (The dwarfs do not know how many of the ten hats are red or blue.) Each dwarf takes a hat and must leave the cave and then organize themselves in separate groups of red- and blue-hatted. If there is one dwarf with a wrong-colored hat in the wrong group - all dwarfs explode, sadly.
Remember, the dwarfs do not know how many of the ten hats are colored red and blue. They also do not know what color hat they have on their head. They are also not allowed to communicate with one another in any way once they leave the cave. The dwarfs can come out individually or as a group. The dwarfs are smart and discuss a fool-proof way in the cave to divide their group into red-hatted and blue-hatted dwarfs. What is it?
#2 River Crossing
Four men are on one side of a river and they want to cross by a rope bridge. The bridge is only strong enough so that 2 men can cross at a time. It is night so the men need to carry a flashlight every time they cross, but they have only one flashlight. Each of the men cross at a different speed. If 2 men cross at the same time the pair must cross together at the slower man's pace. They take the following time to cross the bridge:
#1: 1 minute
#2: 2 minutes
#3: 5 minutes
#4: 10 minutes
What is the shortest time it would take for all four men to cross the bridge?
#3 Scales
Suppose you have a rock that you need to weigh precisely. You know the weight is an integer between 1 and 100, and you have a balance scale. You can go to a store once to buy any set of weights. The question is, what is the minimum number of weights you need to buy to guarantee that you can measure the rock's weight?
Some of the brainteasers that I came across, which I thought worthy to write down. Who knows, they may come in handy...
#1 Dwarves in a Cave
There are ten dwarfs in a dark cave. Inside the cave are ten dwarf hats - five red and five blue. (The dwarfs do not know how many of the ten hats are red or blue.) Each dwarf takes a hat and must leave the cave and then organize themselves in separate groups of red- and blue-hatted. If there is one dwarf with a wrong-colored hat in the wrong group - all dwarfs explode, sadly.
Remember, the dwarfs do not know how many of the ten hats are colored red and blue. They also do not know what color hat they have on their head. They are also not allowed to communicate with one another in any way once they leave the cave. The dwarfs can come out individually or as a group. The dwarfs are smart and discuss a fool-proof way in the cave to divide their group into red-hatted and blue-hatted dwarfs. What is it?
#2 River Crossing
Four men are on one side of a river and they want to cross by a rope bridge. The bridge is only strong enough so that 2 men can cross at a time. It is night so the men need to carry a flashlight every time they cross, but they have only one flashlight. Each of the men cross at a different speed. If 2 men cross at the same time the pair must cross together at the slower man's pace. They take the following time to cross the bridge:
#1: 1 minute
#2: 2 minutes
#3: 5 minutes
#4: 10 minutes
What is the shortest time it would take for all four men to cross the bridge?
#3 Scales
Suppose you have a rock that you need to weigh precisely. You know the weight is an integer between 1 and 100, and you have a balance scale. You can go to a store once to buy any set of weights. The question is, what is the minimum number of weights you need to buy to guarantee that you can measure the rock's weight?