Puzzle Sum 18
What two American cities do these puzzle sums represent?
SOLUTION
NEST + ONE – STONE + WHEEL – HEEL + ARK = NEWARK
WHEEL + PIE + RING – PIER = WHEELING
Category: Puzzles
Samuel Loyd (1841 – 1911), born in Philadelphia and raised in New York City, was an American chess player, chess composer, puzzle author, and recreational mathematician. As a chess composer, he authored a number of chess problems, often with interesting themes. At his peak, Loyd was one of the best chess players in the US and was ranked 15th in the world, according to chessmetrics.com.
MLN
This puzzle/game is played with groups of people, in which at least one of the participants knows the meaning of “MLN”, and the others are trying to figure it out.
All players must sit in a circle, facing each other. Then the people, who do not know what “MLN” stands for, take turns to ask questions. Every question must start with “Is MLN…” and must have a “yes” or “no” answer. Then a player who knows the meaning of “MLN” answers the question and the game continues until everyone solves the puzzle.
To play this game with your friends, at least one of you must know about the solution, which is explained below. Just keep in mind that whoever reads it, will lose the enjoyment of figuring it out by himself.
SOLUTION
The abbreviation “MLN” stands for “My Left Neighbor”. For example, if someone asks “Is MLN a boy?”, the answer will depend on the gender of the person on their left side. This makes the game both interesting and confusing.
68 Coins, 100 Weighings
You have 68 coins with different weights. How can you find both the lightest and the heaviest coins with 100 scale weighings?
SOLUTION
1. Compare the coins in pairs and separate the light ones in one group and the heavy ones in another. (34 weighings)
2. Find the lightest coin in the first group of 34 coins. (33 weighings)
3. Find the heaviest coin in the second group of 34 coins. (33 weighings)
Bridge Over the River
Pinkbird is trying to get to Redbird across the river. Where should we place the bridge, so that the path between the two birds becomes as short as possible?
Remark: The bridge is exactly as long as the river is wide, and must be placed straight across it. Additionally, it has some positive width.
SOLUTION
Notice that no matter how the bridge gets placed over the river, the shortest path would be to go to its top left corner, then traverse it diagonally, then go from its bottom right corner to Redbird. The second part of the way has fixed length, so we must minimize the first part plus the third part. In order to do that, imagine we place the bridge, so that its top left corner is at the current position of Pinkbird – point A. If the bottom right corner ends up at point C, then we must connect C with the position of Redbird – point B, and wherever the line intersects the bottom shore – point D, that will be the best place for the bottom right corner of the bridge.
FEATURED
Balloon in a Car
You are sitting in a motionless car, which is tightly sealed, i.e. no open windows, holes in the car, etc. A helium balloon on a string is tied to the floor. If you start accelerating the car, is the balloon going to move back, forward, or stay in place?
SOLUTION
The reason the balloon floats up in the air is that the helium has a lower density, so when gravity pulls the denser air around down, the balloon gets pushed up. Similarly, when the car accelerates, the air around gets drawn to the back of the car, which makes the helium balloon go forward.
The Gingerbread Dog
Can you cut Sam Loyd’s gingerbread dog into two identical pieces?
SOLUTION
The solution is shown below.
Turns Maze
Enter the maze from the bottom and exit through the top. Turn right at every right square, turn left at every blue square, and go straight through every yellow square.
SOLUTION
The solution is shown below.
Stopped Wall Clock
Ben has a wall clock in his room, but he didn’t wind it one day, so it stopped working. Later that day he left his house, walked to his best friend’s place, who has his own, always precise clock, stayed there for a while, then walked back home. When he arrived, he went to his wall clock and adjusted it to show the correct time. How did Ben do it, if he didn’t see any other clocks during the day, except for the one at his best friend’s place?
SOLUTION
Before Ben left his place, he winded his clock. When he went to his friend’s place, he noted for how long he stayed there, say X, and at what time he left, say Y. After Ben got back home, he looked at his own wall clock and calculated the time he was outside, say Z. Then he concluded that the time he was walking was Z – X in total, and therefore it took him (Z – X)/2 time to get from his friend’s place to his own house. He added Y (the time he left his friend’s place) and got Y + (Z – X)/2, the correct time.
Mate in 1
White to move and mate in 1.
Remark: There is only one correct answer.
SOLUTION
The answer is Qa3#.
FEATURED
Princess in a Palace
A princess is living in a palace which has 17 bedrooms, arranged in a line. There is a door between
SOLUTION
You knock on doors:
2, 3,…, 15, 16, 16, 15,…, 3, 2.
This adds up to a total of 30 days exactly. If during the first 15 days you don’t find the princess, this means that every time you were knocking on an even door, she was in an odd room, and vice versa. Now it is easy to see that in the next 15 days you can’t miss her.