Mathematical Puzzle
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According to the traditional song, on the first day of Christmas (25th December), my true love sent to me:
. A partridge in a pear tree
On the second day of Christmas (26th December), my true love sent to me THREE presents:
. Two turtle doves
. A partridge in a pear treeOn the third day of Christmas (27th December and so on) my true love sent to me SIX presents:
. Three French hens
. Two turtle doves
. A partridge in a pear treeThis carries on until the the twelfth day of Christmas, when my true love sends me:
Twelve drummers drumming
Eleven pipers piping
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five gold rings
Four calling birds
Three French hens
Two turtle doves
A partridge in a pear treeAfter the twelve days of Christmas are over, how many presents has my true love sent me altogether?
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What do the numbers 11, 69, 88, and 96 all have in common?
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Say you have some bendable wires (any number, any length). What is the minimum number of solder connections needed to make a cube? Prove it. Also, what is the minimum number of wires necessary? Prove it.
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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.
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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 chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
How many chickens does farmer John have?
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John walks over a railway-bridge. 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 railway-bridge?
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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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