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.
Category: Puzzles
DescriptionDave Phillips is a maze and puzzle designer, and writer of The Zen Of The Labyrinth—Mazes For The Connoisseur. Phillips has provided puzzles for Reader's Digest, Highlights, National Geographic World, Die Zeit, Ranger Rick, Omni, Games, Scientific American, and United Features Syndicate.
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.
The Lion and the Zebras
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:
- In a lion move, the lion moves from its current position to a position at most 100 meters away.
- In a zebra move, one of the 100 zebras moves from its current position to a position at most 100 meters away.
- The lion wins the game as soon as he manages to catch one of the zebras.
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?
SOLUTION
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,
Source:
Trick Mules
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
SOLUTION
The solution is shown below.
Rich and Poor
Who is richer – the richest among the poor or the poorest among the rich?
SOLUTION
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.
1988 Pennies
Why are 1988 pennies worth more than 1983 pennies?
SOLUTION
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.
Maze Design
How can you design a maze in just 10 seconds, which can not be solved in under 5 seconds?
SOLUTION
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.
Square Cake
There is a square cake at a birthday party attended by a dozen people. How can the cake be cut into twelve pieces, so that every person gets the same amount of cake, and also the same amount of frosting?
Remark: The decoration of the cake is put aside, nobody eats it.
SOLUTION
Divide the boundary of the cake into twelve equal parts, then simply make cuts passing through the separation points and the center. This way all tops and bottoms of the formed pieces will have equal areas, and also all their sides will have equal areas. Since all pieces have the same height, their volumes will be equal as well.