Shoot, Hang, Dinner
A woman shoots her husband, then holds him under water for five minutes, then hangs him, and finally
SOLUTION
The woman takes a picture of her husband and develops it in a dark room.
Category: Puzzles
We do not know where this puzzle originated from. If you have any information, please let us know via email.
FEATURED
King’s Route
A chess king starts on one cell of a chessboard and takes a non-intersecting tour, passing through each square once, and ending up on the initial square. Show that the king has made no more than 36 diagonal moves.
SOLUTION
The king must visit the 28 perimeter squares in order; otherwise, he will create a portion of the board which is inaccessible for him. However, he can not travel from one square to a neighboring one using only diagonal moves. Therefore, he must make at least 28 horizontal/vertical moves and at most 64 – 28 = 36 diagonal moves.
FEATURED
Puzzle Tournament 1
Our first puzzle contest is officially over. Congratulations to the winner Kuan L.!
Also, special thanks to Rajesh Kumar, Johann Sturcz, Dave Phillips, P. A. Heuser, as well as ThinkFun and Dover Books for contributing puzzles.
Time for work – 1 hour
1. Connections
Examine the diagram and find which pairs of letters are connected with each other.
2. King Kong’s Maze
Detective Roy Omoshi (upper right) is chasing a dangerous criminal (lower left) through a destroyed maze. King Kong is trying to help Roy by putting together all the pieces of the maze
3. Color Path
Enter by the bottom red path and exit from the top of the maze. You may retrace your path, but you may not make a U-turn on a pathway. You must follow the paths in the order red, blue, yellow, and then red, blue, yellow again, changing color at the white squares.
4. Amy’s Cats
Aunt Amy’s six cats have sat around the carpet, next to the thread, the pot, the cage, the coffee, the shoes, and the aquarium. You know that:
- The two cats with bows sit next to each other.
- The cats next to the bird cage and the coffee do not have blue eyes.
- The two striped cats sit next to each other.
- The weights of the cats next to the aquarium and the shoes do not differ by more than 3lbs.
- There is a cat with a bell between two cats without long hair.
- Pip Squeak sits next to Tom or Sassy (or both).
Find the names of the cats clock-wise around the carpet, starting from the left.
5. Chess Connect
The starting and ending positions of 7 chess pieces are shown on the board. Find the trajectories of the pieces, if you know that they do not overlap and completely cover the board.
Notes: The pieces can not backtrack. Two trajectories can intersect diagonally but can not pass through the same square. Only the Knight’s has a discontinuous trajectory.
6. Sheep and Wolves
A shepherd takes his two sheep every day to a 7×7 lawn, so that they can eat the fresh grass there. However, there are five wolves on the lawn which are preying on the poor sheep. The shepherd decided to build a closed, non-intersecting fence around the sheep, so that all wolves end up on the outside. He planned the shape of the fence carefully and installed several signs showing the number of fence pieces around the corresponding cells. Can you figure out the shape of the fence the shepherd is going to build?
Solutions
Chords Maze
Find your way from one loose end to the other, following the strings as they pass over and under each other. The knots are three-way intersections.
SOLUTION
The solution is shown below.
How many moves?
If Black just made a move in this game, what is the minimum amount of moves that have been played?
SOLUTION
8 moves example:
1. f3 Nf6
2. Kf2 Ng8
3. Ke3 Nf6
4. Kd3 Ng8
5. Ke4 Nf6
6. Ke3 NNg8
7. Kf2 Nf6
8. Ke1 Ng8
In order to see that 8 is the minimum number of moves, notice that Black could only move rooks and knights, and therefore he has made an even number of moves. This implies that White has made
Gunshots
Two gunshots were fired through the window of a coffee shop. When the police arrived, they successfully recognized which gunshot was fired first. Which was the first gunshot and how did they figure that out?
SOLUTION
The cracks of the left gunshot end up right at the cracks of the right gunshot. Therefore the first gunshot is the one on the right.
So many eights!
Can you draw uncountable many non-intersecting “8” shapes in the plane (they can be contained in one another)?
SOLUTION
No, you can’t. For each “8” shape you can choose a pair of points with rational coordinates – one in its top loop and one in its bottom loop. Since no two “8” shapes can have the same corresponding pair of rational points, their number should be countable.
Royal Wedding
A prince decides to get married to the prettiest girl in his kingdom. All 100 available ladies go to the palace and show themselves to the prince one by one. He can either decide to marry the girl in front of him or ask her to leave forever and call the next one in line. Can you find a strategy which will give the prince a chance of 25% to get married to the prettiest girl? Can you find the best strategy?
Remark: Assume that the prince can objectively compare every two girls he has seen.
SOLUTION
A strategy which ensures a chance of 25% is the following:
The prince banishes the first 50 girls which enter the palace and then gets married to the first one which is prettier than all of them (if such one arrives). If the prettiest girl in the kingdom is in the second 50, and the second prettiest girl is in the first 50, he will succeed. The chance for this is exactly 25%.
The best strategy is to wait until ~1/e of all girls pass, and then choose the first one which is more beautiful than all of them. This yields a chance of ~37% for succeeding. The proof is coming soon.
Puzzle Giveaway 1
Our first puzzle giveaway is over. The winner, Ankush S., is not living in the US, so he decided to donate his prize to a children’s home in Illinois! As an appreciation for his gesture, we created one of our signature avatars for him. Congratulations!
Solve the puzzle below and post the answer on our Facebook page, for the chance of winning the puzzle game Cat Crimes, provided by our friends at ThinkFun.
On the image below you can see 11 points in the plane placed in such
SOLUTION
CAT = 3, BOWL = 2, FISH = 1. The scratches represent Roman numerals.
4 (CAT with a FISH) + 6 (VI) + 2 (TWO FISH) = 12
1 (FISH) + 2 (BOWL) + 5 (CAT with a BOWL) = 8
5 (CAT with a BOWL) + 3 (CAT) + 3 (III) = 11
Therefore, the correct answer is 4 + 2 + 3 = 9.
Six Coins
Take six coins and arrange them in a triangle as shown in the image. Your goal is to rearrange the coins into a hexagon with only four moves. Every move consists of sliding one coin to a new location where it touches at least two other coins.
SOLUTION
The solution is shown below.
