The letters from the three words below can be taken apart, unscrambled and merged to form three separate words all of which are synonyms. Can you find them?

CLIMBER MONITOR NIECE

AnswerIMBECILE MORON CRETIN

 

2. Unscramble

The king of conundrums lives in the MANLIEST CAGE

Answer      ENIGMA CASTLE

 

3. Something Fishy!?
How long does it take for you to solve weird riddles? Time is passing as we speak...tic...toc! This one involves absolutely no academia. If you don't solve it you might be ill. As far as difficulty is concerned it's my easiest one. Can you solve this?

Answer      Scales. The true question is in the title. Take the last letter from each sentence and you have something that's definitely fishy! The second sentence with it's broken text is a subtle hint that something's up with this paragraph.

 

4. SO!

What color is her blouse?

Answer      Blue. Remove the letters "s" and "o" from the word "blouse" and you have the word "blue." Once again it's all in the title.    

 

5. Below there are sixteen numbers. Assuming that any three of the numbers may be drawn at random, what is the probability (to the nearest percent) that three numbers will be drawn whose sum equals six?

1 2 3 1

2 3 1 2

3 1 2 3

1 2 3 1

Answer     
29%
 

6. Judy is five times as old as Henry. In two years, she'll be three times as old, and in six years she'll only be twice as old. How old will Judy be in seven years?

Answer      Judy will be 17 in seven years.

 

7.

ETS

Which one is the odd one out?

URN URA ARS RTH TER NUS

Answer      URA. The other three-letter sets are the last three letters in the names of the planETS (SatURN MARS EaRTH JupiTER and UraNUS). URA is the first three letters in the name of the planet Uranus  

 

8. LET'S SPLIT

Maxwell Edison is studying a newly discovered hyperactive amoeba which multiplies at a highly accelerated rate. He places one such amoeba in a jar. After 15 seconds the amoeba splits. 15 seconds later the two amoebae split. 15 seconds after that the four amoebae split and so on. After two hours the jar is halfway full. How long will it take to fill the jar completely?

Answer 15 seconds after the jar is halfway filled (two hours and 15 seconds after the first amoeba is placed into the jar) the jar will be completely filled. Remember, the amoebae double every 15 seconds.

 

9. GOOD SAMARITAN

463512=a divine service and 3/8 of me is a system or theory. What am I?

Answer altruism. 463512=RITUAL. An ism is a system or belief.

 

10.  Below there are 36 numbers.  Assuming that any three of the numbers may be drawn at random, what is the probability (to the nearest percent) that three numbers will be drawn whose sum equals 15?

456745
567456
674567
745674
456745
567456

Answer17%

 

11. Orgm lif sca means "work all day."

Habba sca flib means "car does work."

Flib clop orgm means "all she does."

What words would you use to say: "Does she work?" The order that you place the words in is unimportant - you only need to find the correct words to use.

AnswerFlib clop sca.

 

12. There are 2 identical strings. If you light one of the strings at its end, it will take exactly one hour for it to finish burning completely. The string will not burn evenly - it is thicker in some places, thinner in others. For example, the string may not be half consumed exactly 30 minutes from lighting it at one end. You have no other means of telling time, and you want to know when exactly 45 minutes have passed. All that you have is a lighter and these 2 identical strings. What is the most accurate method you can use, given these conditions?

AnswerThis method is of course not accurate to the exact millisecond, but it works: Lay the 2 strings out so that they are parallel and stretched all of the way out. There would have to be a few inches between them, but they should be as perfectly matched up side-by-side as possible. You light one string at both ends. It will burn out completely in 30 minutes. The exact point where it burns out - where the 2 flames from the 2 ends meet - you light that EXACT point on the other string, which is lying right next to the first string. You then quickly light both ends of the string. Now that string should be completely consumed in 15 minutes, for a total of 45 minutes. The point you light on the second string is crucial because it is the ACTUAL half way point of the string, as far as burn time goes. This is the answer submitted by a Puzz.com Puzzle Newsletter reader:

"A slightly more elegant solution to question 13 (the strings that must burn in 45 minutes) and that allows for the strings NOT to be identical (but still burn unevenly in 1 hour) is as follows:

Lay the two strings out so they don't touch. Light both ends of string "A", and one end of string "B". When string "A" has burned out, exactly 30 min have gone by, which means that string "B" has exactly 30 min left to burn. Light the other end of string "B". It will now burn out twice as fast in exactly 15 min. The total burning time is 45 min."

For the four puzzles below, pretend you are an alien who had managed to learn the English language, but you do not know what significance the days of the week have. On which day of the week would you assume.

 

13. You would cook a meal.

AnswerFriday

 

14. You would get paid.

AnswerMonday

 

15. You would get married.

AnswerWednesday.

 

16. It would be unusually bright.

Answer Sunday.

 

17. If there are 4 empty seats in a movie theatre, how many permutations are there for the number of ways 4 people could sit in these seats?

Answer24. The answer can be found by starting with 4 numbers or letters, such as 1234, & counting upward using only these 4 numbers to find all of the possible permutations: 1234, 1243, 1324, 1342, etc.

 

18. There are 10 socks of each of the following colors in a drawer: blue, green, red, yellow & white, for a total of 50 socks. If the socks are randomly distributed in the drawer (i.e. not in pairs or any other grouping), & you are blindfolded, what is the minimum number socks you must draw from the drawer in order to be certain you have at least 2 socks of the same color?

Answer6.

 

19. If you are in the same situation as in the preceding problem, how many socks must you draw from the drawer in order to be certain you have at least 2 socks of different colors?

Answer11.

 

20. If none of the following statements are true, who can we conclude broke the vase?

Mike: Sally broke the vase.

Tom: Mike will tell you who broke the vase.

April: Tom, Mike & I could not have broken the vase.

Chris: I did not break the vase.

Erik: Mike broke the vase, so Tom & April couldn't have.

Jim: I broke the vase, so Tom is innocent.

AnswerChris. If the statement "I did not break the vase" is definitely false, we can be certain that Chris broke the vase. Statements that some individuals "couldn't have" broken the vase only mean that these individuals could have broken the vase, but do not guarantee that they did. Jim's statement that "Tom is innocent" is too vague. We know that Tom is not innocent, but this does not assure us that he broke the vase.

 

21. Make a word from boas that can be used to keep you clean.

AnswerThis was a tricky one. The answer is soap. The b had to be twisted & turned to become a p.

 

22. A man & his family lay out blankets & lie down, watching the sky for hours, even though explosions can be heard nearby. Why?
Hint: The date is important.

AnswerThey are enjoying the fireworks on the Fourth of July.

 

23. A woman steps to the edge of a very high building, & as people look on, she leaps off, & falls several stories. The woman is not injured. Why?
Hint: The woman did not fall on cushions or any other type of softened surface, & was not wearing a parachute.

AnswerThe woman had a bungee cord attached to her.

 

24. A man leaves home one night & drives over a mile to meet a friend for a drink. When the man arrives home, the clock shows a time only five minutes later than when he left. How is this possible?
Hint: There is nothing wrong with the clock, & it consistently shows the correct time.

AnswerThe man left his house just before the clocks were set back 1 hour for daylight savings time in the fall. His wife set the clock to show the correct time.

 

25. A boy enters a room that is filled with adults. He is told by a man that the court has found that his parents have neglected & abused him, & he will be placed in foster care. However, the boy sleeps in the same house with his parents that night & several nights after that. No further mention is made of his move to foster care. Why?

AnswerThe activities in the court room were being filmed as part of a movie. The boy was an actor in the movie.

 

26. Three men enter a room filled with gas wearing gas masks. The men voluntarily remove their masks, & begin coughing heavily because of the gas. They do not put their masks back on. The men are not suicidal, so why did they do this?

AnswerThis is a regular training exercise for recruits in basic training for the U.S. Army. I understand that some other branches of the military also practice this type of exercise. The gas is tear gas, & does no permanent damage, as far as I know.

 

27. Spike, an adult, brings the paper to Mr. Hopkins every day. Spike is never paid for this. Why does he do this?
Hint: Spike does not have to bring the paper, but he does not do it entirely because he like Mr. Hopkins.

AnswerSpike is Mr. Hopkins' dog.

 

28. Toby is celebrating his birthday with his friends & family at a restaurant. "I'd like to have a beer - the best you've got! Today is my sixteenth birthday," Toby says to the waiter. The restaurant manager & several customers hear what Toby says, but he is still served a beer. Why?
Hint: Toby really is sixteen years old.

AnswerToby & his family & friends are in a country with no legal drinking age, or a drinking age that is much lower than you will find in the United States.

 

29. A woman bets her friends that she can grab the bare wire on a high voltage electric cable & not be injured. How could she possibly do this?
Hint: Electricity of extremely high voltage is flowing through the cable, & cannot be turned off. The cable cannot be cut or removed from the source of electricity.

AnswerIf the woman is not touching anything but the 1 cable, a circuit will not be completed, & she will not be electrocuted. If she jumped or in some other way grabbed the cable while not touching the ground or anything else but the cable, she would be safe.

 

30. The fastest runner in school bets a much slower runner that he can beat him in a sprint to a point that is 100 yards away from them. After considering for a minute, the slower runner agrees to the bet, & wins the race. How did he do it?
Hint: Both students actually ran in the race.

AnswerThe slower runner was walking toward the finish line while considering whether or not to take the bet. When he agreed, he had a sizeable lead on the other runner, & immediately began sprinting toward the finish line.

 

31. Mark's friends & family throw a surprise party for him. Mark is divorced a few months after the party. Why?
Hint: The party was in a town in which Mark does not live.

AnswerMark was out of town on "business" & staying at a hotel, where the surprise party was held. Because he did not think anyone would be in his hotel room, he picked a woman up at a bar & brought her back with him. His wife was not too happy to see this....

 

32. Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision? The trains are on the same track headed in opposite directions (i.e. directly toward one another).

Answer2 2/3 miles. The trains are exactly 4 miles apart. Their combined speed is 15 miles/hour, so it will take them 16 minutes to collide. The first train will have travelled 1 1/3 miles, so 1/3 mile of it will be out of the tunnel in front, & 2/3 mile of it will be out in the back on collision. The other mile of it will be in the tunnel. The second train will have travelled 2 2/3 miles, so only 1/3 mile of it will still be in the tunnel, so 1 2/3 miles of it will be out of the tunnel.

 

33. You have a box that fits inside of a box that fits inside of a box that fits inside of a box that fits inside of a box, for a total of 5 boxes. Assume that no two boxes can fit inside of a box, unless one is inside of the other (e.g. the two smallest boxes could not fit inside of the largest box, unless the smallest box was inside of the second smallest box), & the boxes cannot be altered (e.g. folded, cut, or torn). Using only these 5 boxes, how many different arrangements are there to place a gift in the boxes, if the gift can only be inside of the smallest box that is being used? Example: The gift in the second smallest box inside of the largest box would be 1 arrangement.

AnswerLet's number the boxes 1 through 5. The number of arrangements can be found by counting out all of the possible arrangements of the numbers 1, 2, 3, 4, & 5, but only for those numbers that are in ascending order (1, 2, 3, 4, 5, 12, 13, 14, 15, 23, 24, 25, 34, 35, etc.), for a total of 31 different arrangements.

 

34. Solve the preceding problem for 6 boxes.

Answer63.

 

35. If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the ? in the last set:

Answer30. In each set, the difference between the two leftmost numbers is divided by two, and then multiplied by the sum of the two rightmost numbers. The product is written in the middle for each set.

 

36. You have 1,432 feet of fence that must be strung out in a straight line. A fence post must be placed for every 4 feet of fence, so how many fence posts will be needed?

Answer359. If you answered 358, you must remember that the fence must begin & end with a post, & dividing 1,432 by 4 leaves one end without a post.

 

37. If you take 7, then 17, & then 8 from me, you have 160. But if you take 6, then 17, then 8 from me, you have 170. Finally, if you take 1, then 4, then 1 from me, you have 762. What am I?

Answer This was a tricky problem. The answer is 17625. In the first situation, you take 7, which leaves you with 1625 (taking the in the sense of removing it, & not subtracting it from the number as a whole), subract 17, & you have 1608, then take 8, which leaves you with 160. For the second situation, you take 6 from 17625, which leaves you with 1725. Subtract 17, & you now have 1708, & if you remove the 8, you have 170. In the last situation, remove 1, so you have 7625. Subtract 4, & you have 7621. Remove the 1, & you have 762. This may be the most difficult puzzle on the quiz by far!

 

38. For each of the following equations, letters have been substituted for the numbers. This substitution is consistent throughout all 4 of the equations. Determine what number (from 0-9) is represented by each of the 10 letters.

A. LFOH
B. LTEL + EMAO + LAHF MOST HOST
C. ELRO
D. OTTH + OLRF + LETH MORE FORE

AnswerR=0, L=1, O=2, H=3, F=4, T=5, E=6, A=7, M=8, S=9. The answers to the 4 equations were: A. 8295, B. 3295, C. 8206, D. 4206.

 

39. I281B4

Determine which of the following letters & numbers completes the sequence above:

S 0 V Q U 22

AnswerIf you 'read' the series, it says "I too ate one before." The only option offered that makes any sense is U, or 'you.' Thanks to Julie Brown for spotting a problem that used to be in this problem....

 

40. Without writing anything or using any calculating device, tell me if there are more 2s or 8s to be found in all of the numbers from 1 to 50,000.

AnswerThere are more 2s. Each number from 20,000 to 29,999 begins with a 2, which greatly weights the scale in favor of the 2s. The number of 8s would not begin to catch up with 2s again until you get well into the 80,000s.

 

41. If 2 of the following statements are false, what chance is there that the egg came first? Round to the nearest whole percent. Note: If any part of a statement is false, then the entire statement must be false.

A. The chicken came first.

B. The egg came first.

C. A is false, & B is true.

Answer0%. C must always be false, because it is impossible for A & B to both be false AND C to be true. If C is false, B is also false.

 

42. If everyone in Chinaville owns an even number of dishes, no one owns more than 274 dishes, & no 2 people own the same number of dishes, what is the maximum number of people in Chinaville?

Answer138. The number can quickly be found by dividing the maximum number of dishes, 274, by 2, because half of the numbers are even, & half of them are odd. However, you must also add 1 to the answer to include 0, which is an even number.

 

43. Determine which of the following words does not belong: 

peck rod feed grain gill

Answer Feed. All of the other words are various weights & measures. Another acceptable answer, found by a visitor: GRAIN, "since it's the only word in the group to begin with two consonants."

 

44. If each letter in the following equations represents a number from 1 through 9, determine what number each letter represents.

A. A+A+B+C = 13

B. A+B+C+D = 14

C. B+B+C+D = 13

AnswerA=3, B=2, C=5, and D=4. An alternate answer is A=2, B=1, C=8, and D=3, which was found by Jill (no last name specified) & by Sharon Kienzle. Ms. Kienzle also found A=4, B=3, C=2, & D=5.

 

45. Should the letter I be on the top or bottom row?

A H J K

B C D E F G L M N O P Q R S T U V W X Y Z

AnswerI would be found on the bottom row. The only thing that A, H, J & K have in common is that each one of them has an 'A' sound when pronounced, which is a feature that all of the other letters lack.

 

46. Complete each of the following statements by filling in each ____ with a word. Don't use reference materials on this one!

A. New York is the big ____

B. An ____ a day keeps the doctor away

C. George Washington cut down the ____ tree

D. As American as ____ pie

E. They say that rabbits have excellent vision because they eat ____

AnswerThe answer is apple for A, B & D. The answer for C is cherry, & E is carrots.

 

47. A little girl is in Missouri, & her mother is in California. The little girl is in an accident, & has to be rushed to a nearby hospital. The little girl is the daughter of the nurse who assists her. How is this possible?

Answer This is a minor twist on a famous puzzle. The nurse is the father of the little girl. Many people don't immediately see this because we are socialized to think of women as being nurses, men as being doctors, etc.

Another acceptable answer for puzzle #10, which was sent in by a reader and Mensa member:

"There is one other possible answer to the question. I grew up in Missouri, and there is a town called, oddly enough, California, Missouri (there is also a Florida Missouri, birthplace of Mark Twain!) located near Jefferson City where there would be a hospital. There are no doubt, people who live in California who commute to Jefferson City to work. I know this may be stretching it, but I thought you'd find it interesting anyway."

 

48. You have 8 marbles that weigh 1 ounce each, & 1 marble that weighs 1.5 ounces. You are unable to determine which is the heavier marble by looking at them. You have a weighing scale that consists of 2 pans, but the scale is only good for 2 total weighings. How can you determine which marble is the heaviest 1 using the scale, & in 2 weighings?

AnswerThis answer is for 2 weighings. The problem I originally had posted here was for 3 weighings, but since you can complete the problem with 2 weighings, I list only the most efficient method. Place 3 marbles on each pan. If they balance, remove the marbles from the pans, & place 2 of the remaining unweighed marbles on the pans, 1 on each pan. If 1 is heavier, it is the heavier marble, but if they balance, the remaining unweighed marble is the heavier 1. If your first weighing does not balance, remove the marbles from the lighter pan, & place 1 marble on each pan from the heavier pan. The heavier 1 is the 1.5 ounce marble, but if they balance, then the marble from the heavy pan from the first weighing that was not weighed in the second weighing is the heavy 1.

 

49. A group of 4 people, Andy, Brenda, Carl, & Dana, arrive in a car near a friend's house, who is having a large party. It is raining heavily, & the group was forced to park around the block from the house because of the lack of available parking spaces due to the large number of people at the party. The group has only 1 umbrella, & agrees to share it by having Andy, the fastest, walk with each person into the house, & then return each time. It takes Andy 1 minute to walk each way, 2 minutes for Brenda, 5 minutes for Carl, & 10 minutes for Dana. It thus appears that it will take a total of 19 minutes to get everyone into the house. However, Dana indicates that everyone can get into the house in 17 minutes by a different method. How? The individuals must use the umbrella to get to & from the house, & only 2 people can go at a time (& no funny stuff like riding on someone's back, throwing the umbrella, etc.).

AnswerThere are 2 possible answers, both of which are almost the same:

Answer 1: Andy & Brenda walk together to the house (2 minutes), & Andy returns (1 minute). Carl & Dana walk to the house (10 minutes), & Brenda returns with the umbrella (2 minutes). Andy & Brenda walk to the house again (2 minutes).

Answer 2: Andy & Brenda walk together to the house (2 minutes), & Brenda returns (2 minutes). Carl & Dana walk to the house (10 minutes), & Andy returns with the umbrella (1 minute). Andy & Brenda walk to the house again (2 minutes).

 

50. You are in a room with 2 doors leading out. Behind 1 door is a coffer overflowing with jewels & gold, along with an exit. Behind the other door is an enormous, hungry lion that will pounce on anyone opening the door. You do not know which door leads to the treasure & exit, & which door leads to the lion. In the room you are in are 2 individuals. The first is a knight, who always tells the truth, & a knave, who always lies. Both of these individuals know what is behind each door. You do not know which individual is the knight, or which one is the knave. You may ask 1 of the individuals exactly 1 question. What should you ask in order to be certain that you will open the door with the coffer behind it, instead of the hungry lion?

AnswerThere are 2 possible answers for this puzzle:

Answer 1: You ask 1 of the individuals what the other 1 would say if you asked him or her which door you should open to get to the coffer. In this case, you would open the other door.

Answer 2: You ask 1 of the individuals what the other 1 would say if you asked him or her which door is holding back the hungry lion. In this case, you would open this door.

 

51. You & I come across 3 people, & each 1 is a knight, knave, or normal (normals sometimes tell the truth, & sometimes lie). Exactly 1 of them is a knight, 1 of them is a knave, & the other 1 is a normal. They make the following statements:

A. I love cats.
B. C always tells the truth.
C. A hates cats.

If I bet you $20 that you could not correctly identify which 1 of these people is a knight, which 'horse' would you be wisest to bet on?

AnswerFor the chart below, assume A = knave, I = knight, & O = normal.

A B C
A I O
A O I
I A O
I O A
O A I
O I A

The first condition & the last 2 conditions cannot occur because contradictions would occur. In 2 of the second, third, & fourth possibilities, the knight is A, the person who claims to love cats. You would be wisest to bet on A, as there is better than a 66% chance that that individual is a knight.

 

52. Four individuals made the following statements, & each 1 is a knight or a knave. Which ones are knaves, if any?

A. Hydroponics is a science that deals with fisheries.
B. D always tells the truth.
C. The primary colors in the spectrum are red, yellow, & blue.
D. C always tells the truth.

AnswerAll 4 individuals are knaves. The primary colors are red, yellow & blue for pigments, but for the spectrum they are red, green & blue. This was a tough puzzle if you didn't use reference aids - not many people know these things!

 

53. If you added together the number of 2's in each of the following sets of numbers, which set would contain the most 2's: 1-333, 334-666, or 667-999?

Answer1-333. The reason why is because 200-299 each begins with a 2!

 

54. You have 3 baskets, & each 1 contains exactly 4 balls, each of which is of the same size. Each ball is either red, black, white, or purple, & there is 1 of each color in each basket. If you were blindfolded, & lightly shook each basket so that the balls would be randomly distributed, & then took 1 ball from each basket, what chance is there that you would have exactly 2 red balls, and 1 non-red ball?

AnswerThere are 64 different possible outcomes, & in 9 of these, exactly 2 of the balls will be red. There is thus a slightly better than 14% chance that exactly 2 balls will be red. A much faster way to solve the problem is to look at it this way. There are 3 scenarios where exactly 3 balls are red:

1 2 3
R R X
R X R
X R R

X is any ball that is not red. There is a 4.6875% chance that each of these situations will occur. Take the first 1, for example: 25% chance the first ball is red, multiplied by a 25% chance the second ball is red, multiplied by a 75% chance the third ball is not red. Because there are 3 scenarios where this outcome occurs, you multiply the 4.6875% chance of any 1 occurring by 3, & you get 14.0625%.

 

55. 8 kips & 14 ligs can build 510 tors in 10 hours, & 13 kips & 6 ligs can build 492 tors in 12 hours. At what rates do kips & ligs build tors? Express your answers in tors per hour.

AnswerThis problem can be solved algebraically: 10 (8k + 14l) = 510 and 12 (13k + 6l) = 492. You then isolate 1 variable in 1 equation, & substitute it in the other equation. Kips build 2 tors an hour, & ligs build 2.5 tors an hour.

 

56. If a juggler juggles 4 objects, how many total throws must he or she make before the objects are returned to their original positions (i.e. the original 2 objects in each hand)? The juggler starts out with 2 objects in each hand, & throws 1 object from 1 hand, then another object from the second hand, then the remaining object from the first hand, & so on. Except for the first throw for each hand, there is a moment where the throwing hand no longer holds anything after each throw. You may wish to draw a diagram for this one.

Answer Pretend that A & B are the objects in the juggler's first hand, & C & D are the objects in the juggler's second hand. You thus start out as AB CD, & each step shows the result after each throw (note: some of the objects would not actually reach their destination in the steps in which they are shown arriving):

1. B ACD
2. BC AD
3. C ABD
4. CD AB
5. D ABC
6. AD BC
7. A BCD
8. AB CD

It would take a total of 8 throws to get the objects back into their original positions.

 

57. A poor man wanted to smoke cigarettes, but did not have enough money to buy them. He found that if he collected cigarette butts, he could make a cigarette from every 5 butts found. He found 25 butts, so how many cigarettes could he smoke?

Answer6. The man made 5 cigarettes from the 25 butts, smoked them, and then made an additional cigarette from the 5 butts that were left from the 5 that he made.

 

58. Having just picked some apples from my tree, I placed them in a basket, & took them around to my friends. I ate one, & then gave a third of the remaining apples to my friend Mike. I then drove to Joe's home, but ate two apples along the way. I gave Joe half of the remaining apples. After Joe's I met Christy, & gave her 10 of the remaining apples, which left one apple. I ate this one later. How many apples started out in the basket?

Answer37

 

59. A man and his son were in an automobile accident. The man died in the accident, but his son was rushed to the hospital. Fortunately, the boy was saved by the doctor who operated on him. The boy was the doctor's son. How is this possible?

AnswerThe doctor was the boy's mother.

 

60. In a certain lottery, thirty balls, each one numbered 1, 2, 3......30 are placed in a basket. The basket is shaken, and 5 of the balls are randomly drawn from the basket, and set side by side. The result is a set of numbers in a particular order, such as 14, 26, 2, 9, and 17. If you purchased a ticket that had 5 such numbers in random order, what chance would you have of winning the lottery?

AnswerYou have 1 chance in 17,100,720. The answer can be found by muliplying the chance of the first ball being any particular number, 1/30, by the chance of the second ball being any particular number, 1/29 (since one ball has already been removed from the basket), & then by 1/28, 1/27, & 1/26.

 

61. Andy, Brian, Cedric, and Dave are an architect, a barber, a caseworker, and a dentist, but not necessarily in that order. Given the following facts, determine what each man's occupation is:

A. At least one, but not all of the men's names begin with the same first letter as their occupation.
B. The architect's name does not contain an r.
C. The barber and dentist each have names that share exactly one letter.

Answer
The architect is Andy, the barber is Dave, the caseworker is Cedric, and the dentist is Brian.
 

62. Three men make the following statements regarding a murder that they are suspected of. Two of the men are lying, & one of them is telling the truth. Exactly one of the men is guilty of the crime. Is anyone definitely guilty or innocent? Which individual(s) is most likely to be guilty?

A. I didn't do it.
B. C did it.
C. A did it.

Answer This problem can be easily solved by using a simple diagram:

A B C

T L L

L T L

L L T

Each L represents a liar, & each T represents the man telling the truth. These are the only three possible permutations for the scenario given. The second permutation is actually not possible, because both A & C's statements cannot both be lies, as A cannot be both guilty & innocent. The first possibility makes B guilty, & the last possibility makes A guilty, so there is a 50/50 chance that A or B is guilty, & C is definitely innocent.