What is the secret in the pattern of this stained glass?
SOLUTION
The image is a superposition of a blue shape and a yellow shape. The places where they coincide are colored in green (blue + yellow = green). The blue shape is consisting of horizontal stripes with lengths 3, 1, 4, 1, 5, 9, 2, 6, 5, representing the number pi, and the yellow shape is consisting of vertical stripes with lengths 4, 6, 6, 9, 2, 0, 1, 6, 1, representing the Feigenbaum constant.
There are five pirates, one monkey, and lots of coconuts on an island. The pirates are supposed to share the coconuts on the next day, but while everybody is sleeping, the first pirate gives 1 coconut to the monkey, splits the remaining coconuts into 5 equal piles, and secretly keeps one of the piles for himself. Later, the second pirate does the same, then the third one, the fourth one, and the fifth one. On the morning, the pirates wake up and split all the remaining coconuts in five, leaving one last coconut for the monkey. What is a possible number for the number of coconuts on the island?
SOLUTION
Notice that if we find a certain number of coconuts which works, then we can add 56 and get a new one. Now imagine the pirates start with -4 coconuts, i.e. they have a total loan of 4 coconuts. Every time a pirate wakes up, he gives 1 coconut to the monkey, which makes the total loan 5 coconuts. Then the pirate keeps a loan of 1 coconut for himself and leaves -4 coconuts. Now we just add 56 coconuts to -4 to make the number positive and get 56 – 4 coconuts as a possible answer.
You have two solid cubes of lead, which have almost the same size. You cut a hole in one of them and pass the other one through it. After measuring the cubes later, it turns out that the larger cube is still heavier than the smaller one. How is this possible?
SOLUTION
You cut a hole in the SMALLER cube, and pass the larger cube through it. “Prince Rupert’s cube” is the largest cube which can pass through a unit cube, and it is approximately 6% larger.
You need to cross a river, from the north shore to the south shore, via a series of 13 bridges and six islands, which you can see in the diagram below. However, as you approach the water, a hurricane passes and destroys some (possibly none/all) of the bridges. If the probability that each bridge gets destroyed is 50%, independently of the others, what is the chance that you will be able to cross the river after all?
SOLUTION
Imagine there is a captain on a ship, who wants to sail through the river from West to East. You can see that he will be able to do this if and only if you are not able to cross the river. However, if you rotate the diagram by 90 degrees, you can also see that the probability that you cross North-South is equal to the probability that he sails West-East, and therefore both probabilities are equal to 50%.
If Erica lives in New York and Tina lives in Buenos Aires, where does Mark live?
SOLUTION
New York is the largest city in the United States of Am-Erica. Buenos Aires is the largest city of Argen-Tina. Therefore Mark lives in Den-Mark’s largest city – Copenhagen.
Suppose you have 10 people with different heights in one row. Show that you can always remove 6 of them, so that the remaining 4 are arranged with respect to their heights (either increasing or decreasing).
SOLUTION
Mark the first person with number 1. Look for the next person after him, who is taller, and also mark him with number 1. Then look for the first person after the second one, who is taller, and also mark him with number 1. If you find a fourth one, then you already got the four people you are looking for.
If not, mark the first unmarked person with number 2. Look for the next unmarked person after him, who is taller, and also mark him with number 2. Continue with the procedure, until you either find 4 people in the line, whose heights are increasing, or have people who are marked with numbers 1, 2, 3 and 4.
Now pick a person, who is marked with number 4. Then look for the closest person on the left, who is marked with number 3, pick him up. He will be taller, because otherwise the first person would have been labeled 3 as well. Similarly, look for the closest person, marked with 2, on the left of the last one, pick him up. Repeat this once again and you will find 4 people in the line, whose heights are decreasing.
In order to catch the thief, you must make your way through this Tetris maze formed by the 5 different pieces shown at the bottom. You can not climb over the blocks, just find a tunnel inside the construction.
Strata is a beautiful award-winning game with mesmerizing sound and unique puzzle concept. It contains hundreds of levels with common rules and final goal. Below I present you these rules and ask you to find a universal algorithm, which will allow you to solve easily every single level of the game.
The rules are simple – you begin with an nxn board, some squares of which are colored in arbitrary colors. Then you start placing stripes of whatever color you choose over entire rows and columns of the board. Your task is after placing all available 2n stripes, the color of every (colored) square to match the color of the stripe which has been placed second over it (on top).
Can you find a simple algorithm, which results in solving any level of the game, no matter the starting position? You can watch AppSpy’s video below for better understanding of the rules.
SOLUTION
Imagine the reverse Strata puzzle – the color of every square must match the color of the first stripe which is placed upon it. Clearly, there must be a line in the grid such that all colored squares in it have the same color. Take all such lines in the grid and place on them stripes of appropriate colors. Then erase the colors from all squares covered by the stripes and repeat the procedure until you place all 2n stripes. It is easy to see that if the reverse Strata puzzle has a solution, then we will find it using this strategy. Finally, in order to solve the original Strata puzzle, just place the stripes in reverse order.
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