The Common One
Kings and queens may cling to power, and the jester’s got his call,
But, as you may all discover, the common one outranks them all.
SOLUTION
The answer is THE ACE IN A DECK OF CARDS.
Category: Puzzles
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Roll a Pencil
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?
SOLUTION
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.
Divine Bell
Can you see which letters are connected with each other in this 3D maze?
SOLUTION
The solution is shown below.
Truck Too Tall
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?
SOLUTION
He deflated slightly the tires of the truck.
Cut the Paper
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
SOLUTION
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.
Pac-Men Maze
Find a path between the two Pacmen in this double-sided maze. You can not switch between the top and the bottom sides of the path you are traversing.
SOLUTION
The solution is shown below.
The Person Who Makes It
The person who makes it, sells it.
The person who buys it, doesn’t use it.
The person who uses it, doesn’t know he is using it.
What is it?
SOLUTION
The answer is COFFIN.
Securing the Box
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.
SOLUTION
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.
Relabeling Dices
Can you relabel two 6-sided dices, so that every face has
SOLUTION
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.