shortest time needed for all four of them to cross the bridge?

Puzzle: -

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

Solution:-

It is 17 mins.
1 and 2 go first, then 1 comes back. Then 7 and 10 go and 2 comes back. Then 1 and 2 go again, it makes a total of 17 minutes.

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probability that none of the ants collide?

Puzzle:-

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

Solution:-

So let’s think this through. The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will definitely be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one in two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.

P(No collision) = P(All ants go in a clockwise direction) + P( All ants go in an anti-clockwise direction) = 0.5 * 0.5 * 0.5 + 0.5 * 0.5 * 0.5 = 0.25

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the total distance traveled by the bee.

Puzzle :-  

Two trains are on same track and they are coming toward each other. The speed of first train is 50 KMs/h and the speed of second train is 70 kmph. A bee starts flying between the trains when the distance between two trains is 100 km. The bee first flies from first train to second train. Once it reaches the second train, it immediately flies back to the second train … and so on until trains collide. Calculate the total distance traveled by the bee. Speed of bee is 40 kmph.

Solution :-

Let the first train moves at u km/h

second train moves at v km/h

distance betweem trains be d km

speed of bee is b km/h

time taken by trains to collide = d/(u+v)

distance travelled by bee = b*d/(u+v) = 40 * 100/(50+70) = 33.333

Please write comments if you find anything incorrect, or you want to share more information about this  topic .

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