2.   The inhabitants of Nathan are of either type A or type B.  Type A people can ask only questions whose correct answer is "yes."  Those of type B can ask only questions whose correct answer is "no."  Benny was overheard to ask, "Are Kitty and I both type B?"  Which type is Kitty? 

3.   An archeologist walking along the shore of the River Nile finds an old Roman coin.  One one side is the face of Julius Caesar and the date 44 BC.  On the other side is an olive tree.  The archeologist says, "This coin is counterfeit."  How does she know? 

4.   There are nine coins in a bag.  One of them is counterfeit.  A real coin weights one gram and a counterfeit one weighs 0.9 gm.  You have a balance.  How can you identify the counterfeit coin with two weightings?

5.     In a remote village in Sichuan everyone either tells the truth all the time or lies all the time.  An English-speaking traveller encounters two of the villagers and asks Mr A, "Are you a truth teller or a liar"?  Unfortunately Mr A speaks no English, so Mr B translates the question an the answer, and replies to the traveller, "Mr A says he is a liar."  Now, which is Mr B, a truth teller or a liar? 

6.     Two trucks, each moving at 50 km/hr, were approaching each other on the same track.  When they were 100 km apart, a bee on the front of one truck started flying toward the other truck at a steady ground speed of 60 km/hr.  When it reached the other truck, it immediately started back toward the first truck.  It continued to fly back and forth until the trucks collided.  How far did it fly?  Incidentally, the bee escaped. 

7.   I know two goldsmiths.  The little goldsmith is the son of the big goldsmith, but the big goldsmith is not the little goldsmith's father.  Who is the big goldsmith? 

8.   The people who live on the east side of the city of Canton always tell the truth, and the people who live on the west side always lie.  During the day the people mingle on both sides.  What one question can you ask a resident picked at random to determine which side of the city you are in?

9.   A traveller is driving to Taipo.  He comes to a fork in the road and sees a farmer.  The farmer is from one of the two families, one who are truth tellers, and one who always lie.  What question can the traveller, 
knowing this, ask the farmer to find out which is the road to Taipo? 

10.   Please find the words whose initials are on the right side of each equation below.  The first answer is shown.

• 26 = L of the A (Letters of the alphabet)
• 1,001 = AN
• 12 = S of the Z
• 9 = P in the SS
• 32 = DF at which WF
• 90 = D in a RA
• 24 = H in a D
• 29 = D in F in a LY

40 = D and N of the GF

2.    How many cats are in a small room if in each of the four corners a cat is sitting, and opposite each cat there sit 3 cats, and at each cat's tail a cat is sitting?

3.    Not far off shore a ship stands with a rope ladder hanging over her side.  The rope has 10 rungs.  The distance between each rung is 12 inches.  The lowest rung touches the water.  The ocean is calm.  Because of the incoming tide, the surface of the water rises 4 inches per hour.  How soon will the water cover the third rung from the top rung of the rope ladder?

4.    A boy has as many sisters as brothers, but each sister has only half as many sisters as brothers.   How many brothers and sisters are there in the family?

5.    Combine plus signs and five 2s to get 28.  Combine plus signs and eight 8s to get 1,000.

6.    The odometer of the family car shows 15,951 miles.  The driver noticed that this number is palindromic: it reads the same backward as forward.
        "Curious," the driver said to himself.  "It will be a long time before that happens again."
        But 2 hours later, the odometer showed a new palindromic number.
        How fast was the car traveling in those 2 hours?

7.    A factory making measuring equipment urgently needed by a power installation has a brigade of ten excellent workers: the chief (an older, experienced man) and 9 recent graduates of a manual training school.
       Each of the nine young workers produces 15 sets of equipment per day, and their chief turns out 9 more sets than the average of all ten workers.
       How many sets does the brigade produce in a day?

8.    Peter was going home.  He rode halfway - fifteen times as fast as he goes on foot.  The second half he went by ox team.  He can walk twice as fast as that.
       Would he have saved time if he had gone all the way on foot?  How much?

9.    An alarm clock runs 4 minutes slow every hour.  It was set right 3 1/2 hours ago.  Now another clock, which is correct, shows noon.
       In how many minutes, to the nearest minute, will the alarm clock show noon?

10.  Every time Mimi sees a stray kitten she picks up the animal and brings it home.  He is always raising several kittens, but he won't tell you how many because he is afraid you may laugh at him.
       Someone will ask: " How many kittens do you have now?"
        "Not many," he answers.  "Three-quarters of their number plus three-quarters of a kitten."
        His pals think he is joking.  But he is really posing a problem - an easy one.

11.   After a cyclist has gone two-thirds of his route, he gets a puncture.  Finishing on foot, he spends twice as long walking as he did riding.
        How many times as fast does he ride as walk?

2.     Three machine and tractor stations were neighbours.  The first lent the second and third as many tractors as they each already had.  A few months later, the second lent the first and third as many as they each had.  Still later, the third lent the first and second as many as they each already had.  Each station now had 24 tractors.
         How many tractors did each station original have?

3.      Three brothers shared 24 apples, each getting a number equal to his age 3 years before.  The youngest one proposed a swap:
         "I will keep only half the apples I got, and divide the rest between  you two equally.  But then the middle brother, keeping half his accumulated apples, must divide the rest equally between the oldest brother and me, and then the oldest brother must do the same."
          They agreed.  The result was that each ended with 8 apples.
          How old were the brothers?

4.      Two freight trains, each 1/6 mile long and travelling 60 miles per hour, meet and pass each other.  How many seconds is it between when the locomotive pass each other and the cabooses pass each other?

5.      A sportsman jumps off a bridge and begins to swim against the current.  The same moment a hat blows off a man's head on the bridge and begins to float downstream.  After 10 minutes the swimmer turns back, reaches the bridge, and is asked to swim on until he catches up with the hat.  He does, under a second bridge 1,000 yards from the first.
         The swimmer does not vary his effort.  What is the speed of the current?

6.      Two ships leave a pier simultaneously.  Ship A downstream and ship B upstream, with the same speed.  As they leave, a life buoy falls off ship A and floats downstream.  An hour later both ships are ordered to reverse course.  Will ship A's crew be able to pick up the buoy before the ships meet?

7.     Motorboat X leaves shore A as Y leaves B; they move across a lake at constant speed.  They meet the first time 500 years from A.   Each returns from the opposite shore without halting, and they meet 300 years from B.
        How long is the lake and what is the relation between the two boats' speeds?

8.     Solve the equations in your head

6,751x + 3,249y = 26,751;
3,249x + 6,751y = 23,249.

2.    "Your pencils, notebooks, and coloured paper cost $1.70."
       "I bought 2 pencils at 2 cents each and 5 pencils at 4 cents each - and 8 notebooks and 12 sheets of coloured paper, I don't remember the prices. But the bill can't be $1.70." 
       Why not?

3.    A motorcyclist was sent by the post office to meet a plane at the airport.
       The plane landed ahead of schedule, and its mail was taken toward the post office by horse.  After half an hour the horseman met the motorcyclist on the road and gave him the mail.
       The motorcyclist returned to the post office 20 minutes before he was expected.
       How many minutes early did the plane land?

4.    An engineer goes every day by train to the city where he works.  At 8:30 am, as soon as he gets off the train, a car picks him up and takes him to the plant.
       One day the engineer takes a train arriving at 7:00 am, and starts walking toward the plant.  On the way, the car picks him up and he arrives at the plant 10 minutes early.
       When does he meet the car?

5.    Is there a number which when divided by 3 gi es a reminder of 1; when divided by 4, gives a remainder of 2; when divided by 5, gives a remainder of 3; and when divided by 6 gives a remainder of 4?

6.    There is a three-digit number.  If you subtract 7 from it, the result is divisible by 7; if 8, divisible by 8; and if 9, divisible by 9.  What is the number?

2.     If Benny were type A, he wouldn't ask the question.  If he is type B, the answer is "no," so Kitty must be type A.

3.     How did anyone in 44 BC know that the year was 44 BC?

4.     Divide the nine coins into groups of three.  Compare the weights of any two of the groups.  If they balance, the counterfeit coin is the third group.  If not, the counterfeit coin is on the lighter side.  Now you know which group contains the counterfeit coin.  Compare the weights of any two coins in that group.  If they balance, the third coin is the counterfeit.  If not, the lighter coin is the counterfeit.  A little inductive reasoning shows that you can identify one counterfeit among 27 coins with three weightings, one among 81 with four weightings, etc.

5.     If Mr A were either a truth teller or a liar, his answer to Mr B's questions in their native language was, "I am a truth teller."  So Mr B is a liar.

6.     Don't calculate the length of the bee's back-and-forth flight.  Just observe that it flew for one hour, and therefore flew 60 km.

7.     The big goldsmith is the little goldsmith's mother.

8.     Ask, "which side of the city do you live in, this side or the other side?"  If you are on the east side, either a truth-telling easterner or a lying westerner will answer, "This side."  If you are on the west side, either will answer, The other side."

9.     The question is, "which road would a member of your family tell me is the road to Taipo?"  Either a truth teller or a liar will point to the correct road.

10.

Arabian Nights

Signs of the Zodiac

Planets in the Solar System

Degrees Fahrenheit at which Water Freezes

Degrees in a Right Angle

Hours in a Day

Days in February in a Leap Year

Days and Nights of the Great Flood

2.    Four cats, each near the tail of a cat in an adjacent corner.

3.    When a problem deals with a physical phenomenon, the phenomenon should be considered as well as the numbers given.  As the water rises, so does the rope ladder.  The water will never cover the rung.

4.    Four brothers and three sisters.

5.    22 + 2 + 2 + 2 = 28;   888 + 88 + 8 + 8 + 8 = 1,000

6.    The first digit of 15,951 could not change in 2 hours.  Therefore, 1 is the first and last digit of the new number.  The second and forth digits changed to 6.  If the middle digit is 0, 1, 2, ..., then the car travelled 110, 210, 310, ... miles in 2 hours.  Clearly the first alternative is the correct one, and the car travelled 55 miles per hour.

7.    Distributing among the nine young workers the 9 extra sets produced by the chief, the daily average for all ten men is 15 + 1  - 16 sets.  Then the chief turns out 16 + 9  = 25 sets daily, and the entire brigade, (15 x 9) + 25 = 160 sets.

8.    Yes.  He took as much time for the second half of his trip as the whole trip would have taken on foot.  so no matter how fast he train was, he lost exactly as much time as he spend on the train.
       He would have saved 1/30 by walking all the way.

9.    In 3 1/2 hours the alarm clock has become 14 minutes slow.  At noon the alarm clock will fall behind approximately an additional minute.  Its hands will show noon in 15 minutes.

10.  Three quarters of a kitten is one-quarter of Mimi's kittens.  She has 4 x 3/4 = 3 kittens.

11.  He walks one-third of the way, or half as far as he rides, but it takes him twice as long.  Therefore he rides four times as fast as he walks.

2.    The problem can be easily solved backward. 
       39 (first) + 21 (second) + 12 (third) = 72

3.    The youngest brother is 7, the middle brother 10, and the oldest 16.

4.    When the locomotives meet, the cabooses are 2/6 = 1/3 mile apart, and their net approaching speed is 120 miles per hour.  It takes them 1/360 hour = 10 seconds to meet.

5.     The swimmer moves away from the hat for 10 minutes and swims toward it 10 minutes.  At the moment he rejoins the hat, the second bridge has "reached" the hat.  Thus the speed of the current is 1,000 / 20 = 50 yards per minute. 

6.     From the buoy's point of view (floating downstream) the ships move away from it at equal speeds in still water.  Then they return at equal speeds in still water.  Thus the two ships reach the buoy simultaneously.

7.    At first meeting, the boats have travelled a combined distance equal to 1 length of the lake; at second meeting, 3 lengths.  Elapsed time and distance for each is three times as great.  Then at second meeting X has travelled 500 x 3 = 1,500 years.  Since this is 300 yards longer than the length of the lake, the latter is 1,200 yards.
The ration of X's speed to Y's equals the ratio of the distances they travel before their first meeting.

8.    Adding and subtracting the equations we see that the numbers become 10,000, 10,000, and 50,000; and 3,502, -3,502, and 3,502.  Dividing by 10,000, and by 3,502, we obtain:
        x + y = 5; 
         x - 7 = 1.

9.     It will meet 13 ships at sea and 1 in each harbour, a total of 15.  The meetings are daily, at noon and midnight.

2.     Four cents, 20 cents, 8 notebooks, and 12 sheets of paper are all divisible by 4 but 170 cents is not.

3.     The motorcyclist would have taken 20 minutes to go from where he met the horseman to the airport and back.  Thus he was 10 minutes from the airport when he met the horseman.  These 10 minutes plus the 30 minutes the horseman had been riding before they met takes 40 minutes the plane was ahead of schedule.

4.     The car was schedule to reach the station at 8:30 am.  When it met the engineers, it saved 10 minutes - 5 to get to the station and 5 to come back to the meeting point.  Therefore, the engineer met the car at 8:20 am.

5.    There is an infinity of such numbers.  The difference between divisor and remainder is always 2.  Then 2 plus the desired number is a multiple of the divisors given.  The lowest common multiple of 3, 4, 5, and 6 is 60, and 60-2 =58, the smallest answer.

6.    The LCM of 7, 8, and 9 is 504.  this is the answer, since no multiples of it have three digits.