Q. Dana, Maya and Carol live in three different countries: China, England and Canada.
Maya lives neither in Europe nor in China.
Carol lives in Asia.
Where do each of the girls live?


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Ans. Maya lives in Canada.
Carol lives in China.
Dana lives in England.

Q. Four angels sat on the Christmas tree amidst other ornaments. Two had blue halos and two – yellow. However, none of them could see above his head. Angel A sat on the top branch and could see the angels B and C, who sat below him. Angel B, could see angel C who sat on the lower branch. And angel D stood at the base of the tree obscured from view by a thicket of branches, so no one could see him and he could not see anyone either.
Which one of them could be the first to guess the color of his halo and speak it out loud for all other angels to hear? 

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Ans. There are 2 possible solutions:
1. if angels B and C had aureole of the same color, then angel A must have immediately said his own color (other then theirs),
2. if angels B and C had different colors, then angel A must have been silent and that would have been a signal for angel B, who could know (looking at angel C) what his own color is (the other one then C had).

Q. Three Palefaces were taken captive by a hostile Indian tribe. According to tribe’s custom they had to pass an intelligence test, or die. The chieftain showed 5 headbands – 2 red and 3 white. The 3 men were blindfolded and positioned one after another, face to back. The chief put a headband on each of their heads, hid two remaining headbands, and removed their blindfolds. So the third man could see the headbands on the two men in front of him, the second man could see the headband on the first, and the first could not see any headbands at all.
According to the rules any one of the three men could speak first and try to guess his headband color. And if he guessed correctly – they passed the test and could go free, if not – they failed. It so happened that all 3 Palefaces were prominent logicians from a nearby academy. So after a few moments of silence, the first man in the line said: "My headband is ...".
What color was his head band? Why? 


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Ans. The first one (he did not see any head bands) thought this way:
The last one is silent, which means, he does not know, ergo at least one of head bands he sees is white. The one in the middle is silent too even though he knows what I already mentioned. If I had a red head band, the second one would have known that he had a white head band. However, nobody says anything, so my head band is not red – my head band is white.

Q. Three Masters of Logic wanted to find out who was the wisest amongst them. So they turned to their Grand Master, asking to resolve their dispute. “Easy,” the old sage said. "I will blindfold you and paint either red, or blue dot on each man’s forehead. When I take your blindfolds off, if you see at least one red dot, raise your hand. The one, who guesses the color of the dot on his forehead first, wins." And so it was said, and so it was done. The Grand Master blindfolded the three contestants and painted red dots on every one. When he took their blindfolds off, all three men raised their hands as the rules required, and sat in silence pondering. Finally, one of them said: "I have a red dot on my forehead."
How did he guess? 

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Ans. The wisest one must have thought like this:
I see all hands up and 2 red dots, so I can have either a blue or a red dot. If I had a blue one, the other 2 guys would see all hands up and one red and one blue dot. So they would have to think that if the second one of them (the other with red dot) sees the same blue dot, then he must see a red dot on the first one with red dot. However, they were both silent (and they are wise), so I have a red dot on my forehead.

Q. You've got 27 coin, each of them is 10 g, except for 1. The 1 different coin is 9 g or 11 g (heavier, or lighter by 1 g). You should use balance scale that compares what's in the two pans. You can get the answer by just comparing groups of coins.
What is the minimum number weighings that can always guarantee to determine the different coin.


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Ans.
You can distinguish among 3**N cases in N weighings.
There are 54 possible cases in this puzzle [one of 27 coins is heavy or light].
So three weighings [27 cases] won't do it, but four [81 cases] can.

Q. . A man is asked what his daughters look like. He answers, "They are all blondes, but two, all brunettes, but two, and all redheads, but two." How many daughters did he have?



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Ans. Three.. one blonde, one brunette and one redhead.

Q.  Six drinking glasses stand in a row, with the first three full of juice and the next three empty. By moving only one glass can you arrange them so empty and full glasses alternate?


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Ans. Pour the second glass into the fifth glass.

Q.You are in a race and you overtake the person who is in second place. What is your position now?


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Ans.  You are in second place since you overtook the second runner and took her place!

Q. 1. You are at a game show and there are three closed doors. There is a prize hidden behind one of the doors and the game show host knows where it is. You are asked to choose a door. The game show host then opens one of the other two doors showing that it is empty and asks you if you would like to change your selection. Should you stick to your original selection?


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Ans. Solution: It is better if you select the other door. Since there are three doors then there is a 67% chance that you choose the wrong door with your first selection.  If you are wrong the game show host will select the other wrong door since she knows where the prize is hidden. Therefore it is better if you switch to the door which the game show host leaves closed.

Q. I had a lot of fun putting together the following list of words. Can you figure out the rule I used to develop the list? Once you do, have fun creating your own list!

mount, right, left, roll, mote, lick,
lass, over, rate, aunt, rill, arch,
oral, ever, pine, rice, tip, each,
team, rash, sage, ouch, edge, ray,
earn, any


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Ans. Each 3 to 5 letter word, when preceded by sequential letters of the alphabet, will form new words:

amount, bright, cleft, droll, emote, flick,
glass, hover, irate, jaunt, krill, larch,
moral, never, opine, price, q-tip, reach,
steam, trash, usage, vouch, wedge, x-ray,
yearn, zany

Q. Suppose you're in a hallway lined with 100 closed lockers.
You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it (if it's closed) or close it (if it's open). Let's call this action toggling a locker. Continue toggling every nth locker on pass number n. After 100 passes, where you toggle only locker #100, how many lockers are open?


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Ans. Answer: 10 lockers are left open:
Lockers #1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Each of these numbers are perfect squares. This problem is based on the factors of the locker number.
Each locker is toggled by each factor; for example, locker #40 is toggled on pass number 1, 2, 4, 5, 8, 10, 20, and 40. That's eight toggles: open-closed-open-closed-open-closed-open-closed.

The only way a locker could be left open is if it is toggled an odd number of times. The only numbers with an odd number of factors are the perfect
squares. Thus, the perfect squares are left open.

For example, locker #25 is toggled on pass number 1, 5, and 25 (three toggles): open-closed-op

Q. Van Gogh (pronounced "Go") is back, with more of his relatives.

e.g. One of them was a well-known musical cousin from Liverpool, England. His name? Ring Gogh! (Ringo)
From the clues, can you guess the other names?
1. An elderly uncle who plays the numbers game at his community hall.
2. His young nephew who bounces everywhere.
3. A long-lost brother who had been on his yacht exploring a group of islands in the Pacific.
4. An aunt, famous for her milk pudding recipe.
5. His cousin with the skin infection.
6. The teenage niece who wears dark, trendy shades of blue and purple.
7. His Great Uncle Emil, the famous lecturer on self-esteem.
The hint gives the first letter, and number of letters, for each word
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Ans. 1. Bing Gogh (Bingo)
2. Poe-Gogh (Pogo)
3. Archie Pele-Gogh (Archipelago)
4. Sae Gogh (Sago)
5. Impa Tai-Gogh (Impetigo)
6. Indy Gogh (Indigo)
7. Prof. E Gogh (Ego)