Getting Older
If the day before yesterday Tim was 18 years old and next year he will be 21 years old, what is the date today?
SOLUTION
Today is 1st of January.
Category: Puzzles
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Every Song
John: “I know every song in the World.”
Paul: “It can’t be. I bet you don’t know any songs which contain the name of my daughter – Beatrice.”
John accepted the bet and won. Which song did he sing?
SOLUTION
John performed the “Happy Birthday” song.
Along O’Brien’s Bridge
Get from START to FINISH in this landscape maze, created by Matthew Haussler.
SOLUTION
The solution is shown below.
Zombie Attack
Oh no, zombies are attacking your house!
Every second, a new zombie drops down on one of the 9 spots of your lawn, which is currently unoccupied. All zombies move towards your house on the left with constant speed, and each of them needs exactly 1 second to traverse a spot of the lawn. Once a zombie steps out of the lawn, it enters your house and waits there for the others (thus each zombie travels total distance between 1 and 9 spots).
Show that after some time, the total distance traversed by any 1000 consecutive zombies will be within the range of just 50 spots.
Remark: Assume your house can accommodate an unlimited amount of zombies.
SOLUTION
Since the number of zombies on the lawn never decreases, it must stabilize at some point. Therefore after some time T, there will be exactly K zombies on the lawn at all times, 1 ≤ K ≤ 9.
Consider any 1000 consecutive zombies appearing past time T and take a picture of the lawn at the moment each of them gets dropped on it – this makes a total of 1000 pictures. Since on every picture, there are exactly K zombies, we see exactly 1000K zombies on these pictures.
Now notice that almost all of the selected 1000 zombies appear on as many pictures as lawn spots they traverse. The zombies for which this is not true are just the K zombies, which appear on the last picture. We easily see that they have traveled between 1 + 2 + … + K − 1 and (10 − K) + (11 − K) + … + 8 spots more than the number of pictures they appear on.
Similarly, on the 1000 pictures we have taken, there are K−1 additional zombies, which appear multiple times (you can see all of them on the first picture). The total number of times they show up is again between 1 + 2 + … + K − 1 and (10 − K) + (11 − K) + … + 8.
Therefore we conclude that the total distance the selected 1000 zombies travel is equal to 1000K ± {[(10 − K) + (11 − K) + … + 8] − [1 + 2 + … + K − 1]} = 1000K ± (9 − K)(K − 1).Since (9 − K)(K − 1) is a number between 0 and 16, this solves the problem.
Place a Coin
Two friends are playing the following game – taking turns, they place identical coins on a square table, so that no two coins touch each other. Whoever can not make a move, loses the game. Who has a winning strategy?
SOLUTION
The first player has a winning strategy. He just has to place the first coin in the center of the table and then each consecutive one symmetrically opposite to the last coin of his opponent.
FEATURED
Tetris Maze
In order to catch the thief, you must make your way through this Tetris maze formed by the 5 different pieces shown at the bottom. You can not climb over the blocks, just find a tunnel inside the construction.
SOLUTION
The solution is shown below.
Stuck in a Blender
You get shrunk 100 times (preserving your density), then thrown in a blender. You have 2 minutes until the blades of the blender start spinning. How are you going to escape?
SOLUTION
If you get shrunk 100 times, but your density remains the same, your muscles will become so strong relative to your size, that you will be able to jump out of the blender. The reason is that your weight will decrease 1000000 times, but your muscle cross-section just 10000 times.
The Cherries Puzzle
Get a stripe of paper, then cut two holes and two slits in it, as shown on the image below. Then try to attach two large cherries to paper, without tearing it apart.
SOLUTION
Pull the handle in the paper through the holes, attach the cherries, then pull it back up.
Bonded Forever
Get 2 ropes and tie them up around the hands of 2 of your friends, as shown on the picture. Then, let your friends separate from each other, without untying the knots or cutting the ropes.
SOLUTION
The solution is shown below.
Cross – Parallel
This puzzle/game is played with groups of people, in which some of the participants know the rules, and others are trying to figure them out.
All players must sit in a circle, facing each other. Then one person who is familiar with the rules starts by pointing at another and saying “cross-cross”, “cross-parallel”, “parallel-cross”, or “parallel-parallel”. After that, the person who got picked must choose another one and guess which one of the four expressions above he must say. If he gets it wrong, he gets corrected, and then the next person continues. The game ends when everyone finds out what the secret is.
To play this puzzle game with your friends, at least one of you must know the secret rules and solution, which are explained below. Just keep in mind that whoever learns the rules, will lose the enjoyment of figuring them out by himself.
SOLUTION
When you point at somebody, you say “cross-cross”, if yours and the other person’s legs are crossed, “cross-parallel”, if yours are crossed and the other person’s are parallel, etc.