Brain games: puzzles, riddles, and logical games.
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A thousand natives Knights, Knaves and Jokers  Weight: 5 Liked the puzzle: 100% 30.12.2009
A MegaMind was captured and brought to an island where a 1000 natives live. Some natives always tell the truth and some always lie. There is at least one truth teller on the island. The MegaMind was promised to be kept alive if he can point out the liars from the truth-tellers. Every hour, the MegaMind is allowed to call up a number of natives and ask a single question: "How many of you are truth-tellers?" or "How many of you are the liars?" How many hours does the MegaMind need before he can determine the liars/truth-tellers?
Comments:  7 | check your solution  
The telephone cable 2 Geometry puzzles  Weight: 5 Liked the puzzle: 100% 01.01.2010
The Megamind has a square parcel of land of size 1x1 km. Accidentally, he has found out that the devious Occupants had buried a telephone cable through his land and use it for their devious communications. The cable is buried along a straight line crossing the square land plot. After discovering this, the Megamind got his shovel and... paused to think. What is the shortest trench that the Megamind has to dig to find the cable? The trench may be disconnected. The proof of optimality is not required.
Comments:  3 | check your solution  
A game with wooden sticks Games puzzles  Weight: 5 Liked the puzzle: 100% 02.01.2010
Two MegaMinds play a game with 100 wooden sticks. The lengths of the sticks are 1,2,3,...,100 inches. Turn by turn, the players choose three of the remaining sticks which form a triangle, and burn them. The player that cannot make a move loses. Which player has a winning strategy (justify your answer)?
Comments:  3 | check your solution  
A game with sums Games puzzles  Weight: 5 Liked the puzzle: 100% 03.01.2010
Two players play the following game. An even number of cards are arranged in a row. Each card is marked with a real number. Upon his turn, a player takes a card from either end of the row. Whoever collects the greater sum is a winner. Otherwise, a draw is declared. Which player is guaranteed not to lose? What is his strategy?
Comments:  5 | check your solution  
A foreign sentry Knights, Knaves and Jokers  Weight: 5 Liked the puzzle: 100% 04.01.2010
You are standing at the road fork. One of the two roads leads to your destination, but you don't know which one. Fortunately, there is a sentry guarding the intersection. Unfortunately, the sentry can be a knight or a knave, moreover, he is a foreigner. He understands you, but when he responds, he says "uhh" or "err" meaning "yes" or "no", but you don't know what means what. He does not say anything else, and he is standing at attention, not being able to point in the right direction. On top of all this, the sentry is somewhat dumb, i.e. he cannot understand sentences longer than 13 words. You may ask a single question to figure out which way to go. Which question should you ask?
Comments:  1 | check your solution  
The 40th anniversary tournament Algebra, arithmetic  Weight: 5 Liked the puzzle: 100% 05.01.2010
Once upon a time, grandfather Megamind told his grandchildren the following tale: On the 40th anniversary of their town, a soccer tournament was held in the central park. Five teams played with each other, 3 points were given for a win, and 1 point was given for tie. Each team earned a different number of points. The goal total was 40. But most curiously, a team placed higher scored fewer and gave up more goals than a team placed lower. Could such tournament really have taken place or is it possible that the old Megamind finally felt his age?
Comments:  1 | check your solution  
Correct labels Weighing puzzles  Weight: 5 Liked the puzzle: 100% 08.01.2010
There are six weights 1,2,3,4,5,6 grams. They are labeled with numbers 1,2,3,4,5,6. Some may be mislabeled. How can you determine whether all labels are correct using a balance scale? What is the minimal number of weighings?
Comments:  1 | check your solution  
Mad Max Logic puzzles  Weight: 5 Liked the puzzle: 66% 12.01.2010
Mad Max is stuck in a desert. He has a vehicle with an empty 20 liter gas tank and three gas canisters containing 100 liters each. The vehicle cannot carry more than one canister at a time. Mad Max wants to get as far as possible from the starting point. The vehicle takes 1 liter of gas per mile. What is the maximal distance that Mad Max can travel one way? (The proof of optimality is not required).
Comments:  1 | check your solution  
Ladders with missing steps Logic puzzles  Weight: 5 Liked the puzzle: 100% 17.01.2010
To fix his roof, Megamind needs to climb up a ladder. He has found many ladders to choose from, but unfortunately some of them were missing steps. Megamind cannot climb a ladder if it is missing two or more steps in a row. Originally, all ladders had N steps, marked bottom to top. How many different ladders can Megamind climb?
Comments:  3 | check your solution  
The game of 15 Games puzzles  Weight: 5 Liked the puzzle: 50% 20.01.2010
Numbers 1,2,3,...,9 are written on a piece of paper. Two players cover these numbers turn by turn using their colored pegs. A number cannot be covered by more than one peg. The winner should cover three numbers which add up to 15. If a player covered more than three numbers, he wins provided that among the covered numbers there is a triple adding up to 15. Is there a winning strategy in this game? Which player has it?
Comments:  1 | check your solution  
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