Treasure

Rating: *****
This is one real-world application of advanced mathematics.
Here is the puzzle:
A young man was going through the attic of his grandfather's house and found a paper describing the location of a buried treasure on an particular Island. The note said that on the island one would find a gallows, an oak tree, and a pine tree. To locate the treasure one would begin at the gallows, walk to the pine tree, turn right 90 degrees and walk the same number of paces away from the pine tree. A spike was to be driven at that point. Then return to the gallows, walk to the oak tree and turn left 90 degrees and walk the same number of paces away from the oak tree. Drive a second spike in the ground. The midpoint of a string drawn between the two spikes would locate the treasure.

The young man and his friends mounted an expedition to the island but found the oak tree and the pine tree but no gallows. It had withered years ago without a trace. They returned home with the map below and no treasure.

Can you show them where to look for the treasure?

Who lives........

Puzzle:
King makes 1000 soldiers of a defeated army stand in a circle.
He numbers them 1 to 1000.
Starting from 1st soldier, he beheads every alternate soldier till last soldier is left, whom he sets free.
If u were one of those soldiers & given an option to choose number, what number will you be standing at?
(i.e. what is the number of soldier set free?)

Additional: Provide a general formula for any number (N) of soldiers.

Will Justice Ever Be Done ?

It rocks............
Puzzle: On a certain island with 500 married couples. In exactly 50 of those couples, the husband is committing adultery. The way gossip works on this island, everyone is very polite, so no one will tell a wife that her husband is committing adultery, but they will certainly tell her about all the other husbands. So let us suppose that every wife of a cheating husband knows about the other cheating husbands, but not her own. One day, the executioner appears in the town square and says, "Any wife who suspects her husband of cheating shall bring him to me today!" But no one brings a husband forth. The next day, the executioner shows up again, but no husband is brought forth. The executioner is stubborn, and so he comes every day. Is justice ever done?

Umbrella Shortage

A sitter............easy one.....
Puzzle: A group of 4 people, Andy, Brenda, Carl, & Dana, arrive in a car near a friend's house, who is having a large party. It is raining heavily, & the group was forced to park around the block from the house because of the lack of available parking spaces due to the large number of people at the party. The group has only 1 umbrella, & agrees to share it by having Andy, the fastest, walk with each person into the house, & then return each time. It takes Andy 1 minute to walk each way, 2 minutes for Brenda, 5 minutes for Carl, & 10 minutes for Dana. It thus appears that it will take a total of 19 minutes to get everyone into the house. However, Dana indicates that everyone can get into the house in 17 minutes by a different method. How? The individuals must use the umbrella to get to & from the house, & only 2 people can go at a time (& no funny stuff like riding on someone's back, throwing the umbrella, etc.).

The Number On Your Hat

Interesting one............get ur grey cells workin.......

Puzzle:
Archimedes, Boole, and Chebyshev, three perfectly wise thinkers, each has a hat on his head, on which is written some positive integer. The host then announces that the number on one of the hats is the sum of the numbers on the other two hats. The following statements are made:
1. Aristotle: I cannot determine my number.
2. Boole: I still cannot determine my number.
3. Chebyshev: I also still cannot determine my number.
4. Aristotle: My number is 50. Aristotle is correct. From this fact, and from the four remarks, can you determine how Aristotle determined his number, and what the numbers on the other two hats were?

Hat Puzzle one

Puzzle:
There's an old puzzle in which the king blindfolds three ministers, places a white or black hat on each one and removes the blindfolds. "If you can see a black hat, raise your hand", he says. They each raise a hand. "If you can tell what color your hat is, raise your hand." All the hands drop. Then suddenly, one minister raises his hand. What color was his hat?