Today we cover some interesting puzzles.
100 people standing in a circle in an order 1 to 100. No. 1 has a sword. He kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3). All people do the same until only 1 survives. Which number survives at the last?
There are 100 people starting from 1 to 100
Solution:
If we start out with an array of 100 numbers labeled 1 to 100 and sorted,
Then in the first round all even numbers are eliminated from the starting point
In the second round, all odd numbers distance four apart are eliminated from the ending point of the previous round. Since even number of elements were removed and this is an even number of rounds, this is the starting point of the first round again.
In the third round, all odd numbers distance eight apart are removed including the number 1. This leaves the starting point as 9. This leaves 9, 25,41,57,73,89.
In the fourth round, all elements distance sixteen are eliminated. This leaves 9, 41, 73.
In the next round all numbers distance 32 are eliminated. This leaves 9, 73.
In the next round all numbers distance 64 are eliminated. This leaves 73.
What is the smallest perfect square which when turned upside down is another perfect square?
The digits which can be turned upside down and still be readable 0,1,6,8,9. The squares with these digits are 1, 9, 16, 81, 100, 169, 196...
The answer is therefore 196
A Police officer caught four criminals. He plays a game with these four men. He lines up three of the prisoners (A, B, C) in one room and the fourth prisoner(D) is placed in a separate room.
Each prisoner is given a hat to wear. The officer tells them that there are in total two blue hats and two red hats. If any of them can guess the color of the hat they are wearing right, he promises to set all four of them free. They cannot communicate with each other, the only information is that
The prisoner A can see the colors of hats worn by prisoner B and prisoner C.
Prisoner B can ONLY see the color of hat worn by prisoner C.
If A sees B and C and if they are wearing the same hat, then he knows the remaining hats and he succeeds.
If he is silent then B can use this information to know that he is wearing a hat different from C, so all hats are known and he escapes.
4) A climber has a stash of chocolates. He climbs five buildings of 100 stairs each and loses one chocolate on every step whether climbing up or down. At the top of each building, he offloads half of his stash. After descending the last building, he has none left. How many did he start with ?
If we start out with an equation in x as the number of chocolates in the beginning, it gets complicated:
((X - (x-100)/2) -100 -100 - (
(X - (x-100)/2) -100 -100)/2) - ... = 0
On the other hand if we start from the end and calculate backwards, we solve it easier
End # = 0
Top of bldg 5 200, bottom of bldg 5 300
Top of bldg 4 800, bottom of bldg 4 900
Top of bldg 3 2000, bottom of building 3 2100,
Top of bldg 2 4400, bottom of bldg 2 4500
Top of bldg 1 9200, bottom of bldg 1 9300
Smoe ideas on Combination Puzzles
100 people standing in a circle in an order 1 to 100. No. 1 has a sword. He kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3). All people do the same until only 1 survives. Which number survives at the last?
There are 100 people starting from 1 to 100
Solution:
If we start out with an array of 100 numbers labeled 1 to 100 and sorted,
Then in the first round all even numbers are eliminated from the starting point
In the second round, all odd numbers distance four apart are eliminated from the ending point of the previous round. Since even number of elements were removed and this is an even number of rounds, this is the starting point of the first round again.
In the third round, all odd numbers distance eight apart are removed including the number 1. This leaves the starting point as 9. This leaves 9, 25,41,57,73,89.
In the fourth round, all elements distance sixteen are eliminated. This leaves 9, 41, 73.
In the next round all numbers distance 32 are eliminated. This leaves 9, 73.
In the next round all numbers distance 64 are eliminated. This leaves 73.
What is the smallest perfect square which when turned upside down is another perfect square?
The digits which can be turned upside down and still be readable 0,1,6,8,9. The squares with these digits are 1, 9, 16, 81, 100, 169, 196...
The answer is therefore 196
A Police officer caught four criminals. He plays a game with these four men. He lines up three of the prisoners (A, B, C) in one room and the fourth prisoner(D) is placed in a separate room.
Each prisoner is given a hat to wear. The officer tells them that there are in total two blue hats and two red hats. If any of them can guess the color of the hat they are wearing right, he promises to set all four of them free. They cannot communicate with each other, the only information is that
The prisoner A can see the colors of hats worn by prisoner B and prisoner C.
Prisoner B can ONLY see the color of hat worn by prisoner C.
If A sees B and C and if they are wearing the same hat, then he knows the remaining hats and he succeeds.
If he is silent then B can use this information to know that he is wearing a hat different from C, so all hats are known and he escapes.
4) A climber has a stash of chocolates. He climbs five buildings of 100 stairs each and loses one chocolate on every step whether climbing up or down. At the top of each building, he offloads half of his stash. After descending the last building, he has none left. How many did he start with ?
If we start out with an equation in x as the number of chocolates in the beginning, it gets complicated:
((X - (x-100)/2) -100 -100 - (
(X - (x-100)/2) -100 -100)/2) - ... = 0
On the other hand if we start from the end and calculate backwards, we solve it easier
End # = 0
Top of bldg 5 200, bottom of bldg 5 300
Top of bldg 4 800, bottom of bldg 4 900
Top of bldg 3 2000, bottom of building 3 2100,
Top of bldg 2 4400, bottom of bldg 2 4500
Top of bldg 1 9200, bottom of bldg 1 9300
Smoe ideas on Combination Puzzles
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