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A cardinal points and says, “thorn, shout, seat, and stew.” Can you explain?
The sentence is a play on words and anagrams. Thorn, shout, seat, and stew are anagrams of the four cardinal directions of the compass: north, south, east, and west.
There are 100 rooms in a row in a building and inside each room there is a lamp that is turned off. One person enters each room and switches the lamp inside. Then, a second person enters every second room (2, 4, 6, etc.) and switches the lamp inside. A third person switches the lamp in every third room and so on and so far, until person #100 switches the lamp in room 100. How many lamps are turned on at the end?
We can see that the only switches that have been switched an odd number of times are the ones in rooms with perfect square numbers.
Indeed, if person N has switched the switch in room M, then person M/N has done that as well. Since person N and M/N coincide only when M=N², the claim above follows.
We conclude that the number of lamps that are turned at the end is equal to the number of perfect squares less than or equal to 100; that is exactly 10 rooms.
What unique feature do the following words share?
FRIEND, FEAST, THERE, THOROUGH, FLIGHT, WONDERFUL, RESIGN, ENDURING, PEST, COVERT
Each of these words contains its antonym as a sub-word:
FRIEND – FIEND, FEAST – FAST, THERE – HERE, THOROUGH – ROUGH, FLIGHT – FIGHT, WONDERFUL – WOEFUL, RESIGN – REIGN, ENDURING – ENDING, PEST – PET, COVERT – OVERT
People make me, save me, waste me, raise me. What am I?
The answer is MONEY.
A dog was tied to a tree with a 7-meter rope. How did the dog manage to get to its bowl of food which was 15 meters away from the dog?
The dog was initially on the other side of the tree and the tree’s diameter was 1 meter long. Thus, when the dog moved to the opposite side, it got 2×7+1=15 meters closer to its food.
How many pawns can you place at most on a chess board so that no three pawns lie on a single line, horizontal, vertical, or diagonal?
Since there are 8 rows on the chess board, if you place more than 16 pawns, then there will be at least 3 that lie on a single horizontal line. An example with 16 pawns is shown below:
Who have more sisters on average in a society: boys, girls, or is it equal?
Remark: Assume that each child is born a boy or a girl with equal probability, independent of its siblings.
The average number of sisters is roughly the same for both boys and girls. To see this, notice that every girl in every family contributes “one sister” to each of its siblings who are either a boy or a girl with equal probability. Therefore, every girl contributes on average the same number of sisters to the group of boys and to the group of girls. Since there is roughly the same number of boys and girls in the society, the average number of sisters for boys and girls is the same.
A car weighing 1500kg (including the driver) starts crossing a 20km long bridge. The bridge can support at most 1500kg and, above that weight, it collapses. If halfway through the bridge, a small bird, weighing 200g, lands on the roof of the car, will the bridge collapse?
By the time the car reaches the middle of the bridge, it would have used fuel that weighs more than 200g, so the bridge will not collapse.
How many X’s can you place the most on a tic-tac-toe board without getting 3 X’s on a line?
You can place 6 X’s without getting 3 X’s on a line, as shown below.
Suppose you are on a one-way circular racetrack. There are 100 gas cans randomly placed on different locations of the track and the total amount of gas in the cans is enough for your car to complete an entire circle. Assume that your car has no gas initially, but you can place it at any location on the track, then pick up the gas cans along the way and use them to fill the tank. Show that you can always choose a starting position so that you can complete an entire circle.
Imagine you put your car at any location, but instead with an empty tank, you start with enough gas to complete the circle. Then, simply track the amount of gas you have and locate the point on the track where it is the lowest. If you choose that location as a starting point, you will be able to complete the track.
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