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A Game of 49
Start with a 7 by 7 square grid. You can start on any square and you have to make 49 moves. Wow! You move like a knight in chess for each move thereafter. The first move is labeled 1 in the grid, the 2nd 2, etc.. What are the solutions to this "49" puzzle as in what does the grid look like to fill in the whole 7 by 7 square grid?
π°
The High School Lockers Game
There are 500 lockers in a high school. The first student opens every locker. The 2nd student closes every other locker. The 3rd student opens every 3rd closed and closes every 3rd opened locker. The 4th student opens every 4th closed locker and closes every 4th opened locker. Etc. up to the 500th student.
Which lockers are closed and which ones are open? π
Three Daughters Puzzle
https://www.teamten.com/lawrence/puzzles/daughters.html
Geometry Puzzles
https://mathwithbaddrawings.com/2018/10/03/twenty-questions-of-maddening-delicious-geometry/
Some of the solutions are located at the bottom of this page.
A Smart Boy
Three brothers shared 24 apples, each getting a number equal to his age 3 years before. The youngest one proposed a swap:
βI will keep only half the apples I got, and divide the rest between you two equally. But then the middle brother, keeping half his accumulated apples, divide the rest equally between the oldest brother and me, and then the oldest brother must do the same.β
They agreed. The result was that each ended with 8 apples.
How old were the brothers?
The Monkey and the Coconuts
Three shipwrecked sailors and a monkey found themselves on an island where the only food was coconuts. They gathered coconuts all day, and decided to go to sleep and divide them up the next day. During the night one of the sailors woke up and decided to take his share of coconuts rather than wait until morning. He divided the coconuts into three piles, but there was one left over which he gave to the monkey. He hid his pile and went back to sleep. Later, another sailor got up and did the same as the first sailor and went back to sleep. And later on the third sailor woke up and proceeded to divide the coconuts as the other two sailors had done, also giving the left over coconut to the monkey. In the morning, when the three sailors got up, they divided the pile of coconuts into 3 shares with one left over for the monkey.
What is the least number of coconuts the sailors collected?
The Two Tribes
An island is inhabited by two tribes. Members of one tribe always tell the truth, members of the other always lie.
A missionary met two of these natives, one tall, the other short. "Are you a truth-teller?" he asked the taller one.
"Oopf," the tall native answered.
The missionary recognized this as a native word meaning either yes or no, but he couldn't recall which. The short native spoke English, so the missionary asked him what his companion had said.
"He say 'yes'," replied the short native, "but him big liar!"
What tribe did each native belong to?
Three Men Facing the Wall
Three men were placed in a line perpendicular to a wall. They are blindfolded. Then three hats are taken from a bin of three tan hats and 2 black hats. The men are given that information. Then the blindfolds are removed. Each man is asked to determine what color he is wearing.
The man farthest from the wall who sees the two men and their hats in front of him says, βI do not know which color hat I am wearing.β
The second man from the wall who heard the reply and sees the man and hat ahead of him says the same thing. The third man who sees only the wall, but has heard the two replies says,
βI know which color hat I am wearing.β
Which color is he wearing and how did he determine it?
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