Mathematical Puzzle

John and Jacob are on the two opposite banks of a river. They both have a rowing boat.
They both start at the same time towards the opposite bank. They pass each other at 180 meters from the bank where john departed. When reaching the opposite bank, they both take a rest for the same amount of time before they return. On the way back, they pass each other at 100 meters from the bank from where John returned.
John and Jacob both row with a constant speed, but Jacob rows faster.
How wide is the river?
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Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. Assume you have an unlimited number of colour sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?
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In the city of Mexico, the following facts are true:
No two inhabitants have exactly the same number of hairs.
No inhabitant has exactly 483,207 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.
What is the largest possible number of inhabitants of Mexico?View SolutionSubmit Solution 81 views
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Farmer John has a chicken farm. On a certain day, John calculates in how many days he will run out of chickenfood. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chickenfood he has, and that if he would buy 100 extra chickens, he would run out of chickenfood fifteen days earlier.
How many chickens does farmer John have?
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John walks over a railwaybridge. At the moment that he is just ten meters away from the middle of the bridge, he hears a train coming from behind. At that moment, the train, which travels at a speed of 90 km/h, is exactly as far away from the bridge as the bridge measures in length. Without hesitation, John rushes straight towards the train to get off the bridge. In this way, he misses the train by just four meters! If John had rushed exactly as fast in the other direction, the train would have hit him eight meters before the end of the bridge.
What is the length of the railwaybridge?
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Every day, John takes the train to travel from his work back to Mexico City, his place of residence. Usually, he arrives at the station of Mexico at six o’clock, and exactly at that moment, his wife picks him up by car. Yesterday evening, John took an earlier train, without informing his wife, and therefore he already was at the station of Mexico at five o’clock. He decided to walk part of the way to meet his wife. When he met the car with his wife, he drove home with her. In this way, they were home ten minutes earlier than normal. John’s wife always drives the entire way between home and station at the same constant speed.
How long did John walk yesterday evening?
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Jacob & John have two children. The probability that the first child is a girl is 50%. The probability that the second child is a girl is also 50%. Jacob & John tell you that they have a daughter.
What is the probability that their other child is also a girl?
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A school bus travels from Los Vegas to Lo Angels. There are four children in the bus. Each child has four backpacks with him. There are four dogs sitting in each backpack. Every dog has four puppies with her. All these dogs have four legs, with four toes at each leg.
What is the total number of toes in the bus?
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