The Knight’s Tour is a famous chess problem, in which a knight starts on the top-left square of an ordinary chessboard and then makes 63 moves, landing on every square of the chessboard exactly once (except for the starting square).
Can you complete the Knight’s Tour? For a further challenge, can you find a “closed” solution, meaning that the knight can make a 64th move to land back on the starting square (thus making the solution circular)?
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Given 9 Dots, draw 4 Lines without picking up pen
Putting numbers in 3X3 matrix - s.t. Rows OR columns or diagonals add till 15
How can you place the numbers 1 through 9 in a 3x3 grid such that every row, column, and the two diagonals all add up to 15?
Solution It first seems logical to put the 5 in the middle square becuase it is the median and mean of the numbers from 1 to 9 (and also the average of any 3 numbers adding up to 15).
The next thing to do is place the 1 since it’s the smallest and will thus be likely to quickly constrain what we can do afterward.
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Robots on a line
Two robots are placed at different points on a straight line of infinite length. When they are first placed down, they each spray out some oil to mark their starting points.
You must program each robot to ensure that the robots will eventually crash into each other. A program can consist of the following four instructions:
Go left one space Go right one space Skip the next instruction if there is oil in my current spot Go to a label [Note that a “label” is a name that refers to a line of your code.
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Brothers and sisters
Problem You and a friend are standing in front of two houses. In each house lives a family with two children.
“The family on the left has a boy who loves history, but their other child prefers math,” your friend tells you.
“The family on the right has a 7-year old boy, and they just had a new baby,” he explains.
“Does either family have a girl?” you ask.
“I’m not sure,” your friend says.
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Using 5,5,5,5,5 can you make 37 along with any arithmetic operation.
Using 5,5,5,5,5 can you make 37 along with any arithmetic operation.
Make 3 3 7 7 equal to 24
Make 3 3 7 7 equal to 24
Using only and all the numbers 3, 3, 7, 7, along with the arithmetic operations +,-,*, and /, can you come up with a calculation that gives the number 24? No decimal points allowed.
Cards in the Dark
Problem You are standing in a pitch-dark room. A friend walks up and hands you a normal deck of 52 cards. He tells you that 13 of the 52 cards are face-up, the rest are face-down. These face-up cards are distributed randomly throughout the deck.
Your task is to split up the deck into two piles, using all the cards, such that each pile has the same number of face-up cards.
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Islanders with dotted forheads
Problem There is an island with 100 women. 50 of the women have red dots on their foreheads, and the other 50 women have blue dots on their foreheads.
If a woman ever learns the color of the dot on her forehead, she must permanently leave the island in the middle of that night.
One day, an oracle appears and says “at least one woman has a blue dot on her forehead.
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