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.
Can you find the objects which are hidden in the images below?
The solution is shown below.
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.
Find all the hidden words in the grids.
The solutions are 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.
Left alone, I’m a word with five letters.
I’m honest and fair, I’ll admit.
Rearranged, I’m of no use to trains.
Again, and I’m an overt place, warm and well lit.
What am I?
The answer is LIAR. After rearranging the letters, you can get RAIL – important for trains, or LAIR – a dark, hidden place. Since the riddler is a liar, the resulting words are exactly the opposite of his descriptions.
Replace every letter with a different digit between 0 and 9, such that you get a correct calculation.
The answer is 9567 + 1085 = 10652.
You can first see that M = 1. Then S = 8 or 9 and O = 0. MORE is at most 1098, and if S = 8, then E = 9, N is either 9 or 0, but this is impossible. Therefore S = 9, N = E + 1. You can check easily the 6 possibilities for (N, E) and then find the answer.
Imagine you are driving a bus. At the first stop, 3 people get on the bus. At the second stop, 5 more get on. At the third stop, 2 get out and 4 get on. At the last stop, everybody gets out. How old is the bus driver?
You are imagining the story, so the bus driver is as old as you.
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