Take a square (or circle) coaster. Then, cut a hole in a piece of paper with the shape of a square, so that the side of that square is half of the side (or the diameter) of the coaster. Now, your goal is to push the coaster through the hole without tearing the paper (you can fold it).
Coming soon.
A hungry lion runs inside a circus arena which is a circle of radius 10 meters. Running in broken lines (i.e. along a piecewise linear trajectory), the lion covers 30 kilometers. Prove that the sum of all turning angles is at least 2998 radians.
Imagine the lion is static, facing North, and instead, the center of the arena moves around. Then, each time the lion runs X meters in some direction, this translates into the center moving X meters South. Each time the lion makes a turn of Y radians, this translates into the center moving along an arc of Y radians.
Thus, the problem translates to a point inside the arena alternating between traveling straight South and then moving along arcs around the center of the arena. Since the total distance traveled straight South by the point is 30KM and the distance between the starting and the ending points is at most 20M, the total distance traveled North must be at least 30KM – 20M = 29980M. Therefore, the total length of the arcs traversed by the point is at least 29980M, and since the radius of each arc is at most 10M, the total angle of the arcs must be at least 2998 radians. The sum of all turning angles of the lion is the same, so this concludes the proof.
Warning: this puzzle involves mature themes that are inappropriate for younger audiences. If you are not an adult, please skip this puzzle.
Can you find the objects which are hidden in the images below?
The solution is shown below.
Minecraft: Magnetic Travel Puzzle (M:MTP for short) is a travel game by ThinkFun in which the goal is to arrange 3 types of objects, each coming in 3 different colors, in a 3 by 3 grid, such that certain conditions are satisfied.
As you progress through the 40 included challenges, the types of conditions you encounter become gradually more complex. While in the beginning you may be given all the colors of the objects with one clue and all the types of the objects with another, later on you need to analyze 5 or 6 clues at once, which makes the game more challenging and fun. That being said, at the hardest levels, M:MTP is still relatively easy, so experienced puzzlers will probably breeze through it within an hour or two.
At its core, M:MTP is identical to ThinkFun’s previously released Clue Master. Both games are presented in the form of magnetic notebooks, so they are easy to pick up and travel around with. The illustrations of the Minecraft edition are all based on the popular video game, so its fans may be particularly appreciative.
If you are looking for a casual puzzle to pass an hour or two on a road trip, then M:MTP would be a great choice. I only wish there were more challenges included, especially more difficult ones.
Is it possible to connect each of the houses with the well, the barn, and the mill, so that no two connections intersect each other?
No, it is impossible. Here is a convincing, albeit a informal proof.
Imagine the problem is solvable. Then you can connect House A to the Well, then the Well to House B, then House B to the Barn, then the Barn to House C, then House C to the Mill, and finally the Mill to House A. Thus, you will create one loop with 6 points on it, such that houses and non-houses are alternating along the loop. Now, you must connect Point 1 with Point 4, Point 2 with Point 5, Point 3 with Point 6, such that the three curves do not intersect each other. However, you can see that you can draw no more than one such curve neither on the inside, nor the outside of the loop. Therefore, the task is indeed impossible.
More rigorous, mathematical proof can be made using Euler’s formula for planar graphs. We have that F + V – E = 2, where F is the number of faces, V is the number of vertices, and E is the number of edges in the planar graph. We have V = 6 and E = 9, and therefore F = 5. Since no 2 houses or 2 non-houses can be connected with each other, every face in this graph must have at least 4 sides (edges). Therefore, the total number of sides of all faces must be at least 20. However, this is impossible, since every edge is counted twice as a side and 20/2 > 9.
Kuku and Pipi decide to play a game. They arrange 50 coins in a line on the table, with various nominations. Then, alternating, each player takes on their turn one of the two coins at the ends of the line and keeps it. Kuku and Pipi continue doing this, until after the 50th move all coins are taken. Prove that whoever starts first can always collect coins with at least as much value as their opponent.
Remark: On the first turn, Kuku can pick either coin #1 or coin #50. If Kuku picks coin #1, then Pipi can pick on her turn either coin #2 or coin #50. If Kuku picks coin #50, then Pipi can pick on her turn either coin #1 or coin #49.
Let’s assume Kuku starts first. In the beginning, he calculates the total value of the coins placed on odd positions in the line and compares it with the total value of the coins placed on even positions in the line. If the former has a bigger total value, then on every turn he takes the end coin which was placed on odd position initially. If the latter has bigger value, then on every turn he takes the end coin which was placed on even position initially. It is easy to see that he can always do this because after each of Pipi’s turns there will be one “odd” coin and one “even” coin at the ends of the line.
Two trains are crossing the bridge bellow at the same speed on a non-windy day. One of the trains
The two trains have different lengths, so the longer one needs more time until it crosses completely the bridge.
Can you add all 16 black pieces on the board (king, queen, 2 knights, 2 bishops, 2 rooks, 8 pawns) and get a chess position, in which no piece is attacked by another?
Yes, you can, as shown in the diagram below.
There are three playing cards in a row. There is a two to the right of a king. There is a diamond to the left of a spade. There is an ace to the left of a heart. There is a heart to the left of a spade. Identify the three cards.
The cards are an Ace of Diamonds, a King of Hearts, and a Two of Spades.
“The Boat” is a graphic novel adaptation of Nam Le’s book, presented as an immersive webpage experience by Matt Huynh. With beautiful artwork and stunning effects, the novel tells the story of a 16-year old Vietnamese refugee, embarking on a dangerous trip across the sea. Click the banner below and scroll your way through this captivating, moving, and harrowing tale.
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