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You roll a 5 sided pencil on the table. On one of its sides, it is written “HB Pencil”, the others are blank. What is the chance that the side with text on it ends up straight on top?
The chance is 0%. Since the pencil has an odd number of sides, it is impossible that any of them ends up straight on top.
A driver needs to pass under a bridge, but his truck is one inch too tall. However, despite this issue, the driver finds a way to continue further. How?
He deflated slightly the tires of the truck.
You have a sheet of paper and a rectangular piece cut from it, as shown in the picture. What is the easiest way to cut the paper into two pieces with
Make a cut through the centers of the small and the big rectangle. The cut will split both the area of the big and the small (absent) rectangle by half, and therefore will do the same to their difference – the given sheet of paper.
There are 5 people who possess a box. You are allowed to secure the box with as many different locks as you like and distribute any combination of keys for these locks to any people among the 5. Find the least number of locks needed, so that no 2 people can open the box, but any cannot people can open it.
For every subset of 2 people you pick among the 5, there should be a lock which none of the 2 can unlock, and each of the remaining 3 people can unlock. Clearly, the lock in question cannot be the same for any two different subsets of 2 people you choose. Therefore the number of locks you need is at least the number of different 2-element subsets of a 5-element set, which is 5!/(2!3!)=10. This number is sufficient as well – just give keys to a different group of 3 people for every lock.
Can you relabel two 6-sided dices, so that every face has
Yes, you can do this. The easiest way is to use generating functions. Using simple polynomial algebra, you can see that
(x + x2 + x3 + x4 + x5 + x6)2 = (x + 2x2 + 2x3 + x4)(x + x3 + x4 + x5 + x6 + x8).
Therefore, if you take a dice with spots {1, 2, 2, 3, 3, 4}, and a dice with spots {1, 3, 4, 5, 6, 8}, their sum will have the same probability distribution.
The lion plays a deadly game against a group of 100 zebras that takes place in the steppe (an infinite plane). The lion starts in the origin with coordinates (0,0), while the 100 zebras may arbitrarily pick their 100 starting positions. The lion and the group of zebras move alternately:
Will the lion always win the game after a finite number of moves? Or is there a strategy for the zebras that lets them survive forever?
The zebras can survive forever. They choose 100 parallel strips with width 300m each, then start on points on their mid-lines. If the lion lands on some zebra’s strip, the zebra simply jumps 100m away from the lion,
In order to solve this puzzle, you must print the image below and cut it in 3 pieces along the dotted lines. The question is, can you after that rearrange these pieces
The solution is shown below.
Who is richer – the richest among the poor or the poorest among the rich?
The poorest among the rich is richer than the richest among the poor. That is because any rich person is by default richer than any poor person.
Why are 1988 pennies worth more than 1983 pennies?
For the same reason 20 pennies are worth more than 15 pennies. 1983, 1988 are the numbers of pennies, not the years they have been made.
How can you design a maze in just 10 seconds, which can not be solved in under 5 seconds?
Just quickly draw a maze in the shape of a spiral. The other person must be twice as fast as you in order to solve it.
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