Visiting the Mall

Bill, Chuck, Sally, and Dave all went to the mall together last week and entered at the same set of doors between Lord & Taylor's and Abercrombie & Fitch.  Dave wanted to go to the information booth to find out if he could buy mall gift certificates, Bill was hungry and said he needed to get something to eat at the snack bar, and Sally and Chuck needed to use the restrooms.

Can you draw a line from each person to their destination so that no two lines touch or intersect?

The Two Trains

Henry Dudeney recalls, "I put this little question to a stationmaster, and his correct answer was so prompt that I am convinced there is no necessity to seek talented railway officials in America or elsewhere.

Two trains start at the same time, one from London to Liverpool, the other from Liverpool to London.  If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?"

A Strange Safari - Part 2

Earlier in the month we posted a puzzle about Professor Egghead's Australian safari where he, sadly, did not see any animals other than horses and people on his first day.  Luckily the professor did get a chance to see animals on his second day of safari.

After the second day Professor Egghead called me again and this time he was happy to announce that he had seen real wildlife while out riding the horses.  I asked him how many animals he had seen and, again, he didn't remember the exact number of all the animals, but he did remember that, including the horses and people from the day before, there were a total of 52 eyes and 74 legs.

If there were twice as many 4 legged dingoes as there were 2 legged ostriches, how many of each wild animal did the professor see?


(You'll have to be a bit creative to get the right answer to this one.)

The Professor's Wooden Measuring Stick

Professor Egghead was accompanying a colleague on a remote archaeological expedition.  On the first day of the dig, however, he was surprised to discover that he had forgotten some of his tools at home.  Most important of his missing tools was his ruler, used for measuring lengths of small objects uncovered at the dig site.  He was able to find a straight, blank wooden stick that measured exactly 10 inches and borrowed a ruler from one of the other members of the team to make marks on his stick to create a ruler of his own.  To keep things simple the professor wanted to make as few marks on his new ruler as possible.

What is the fewest number of marks the professor could make on the stick so that he could still accurately measure any whole number length from 1 inch to 10 inches?  For instance, placing a mark 1 inch from one end would allow the professor to measure 1 inch and 9 inches.

Weights and Measures

A boy selling fruit has only 3 weights, but with them he can weigh any whole number of pounds between 1 and 13.

What is the measurement of each of his three weights?

Professor Egghead's Horse

Professor Egghead bought a horse for 60 Euros.  He later sold the horse to his neighbor for 70 Euros, but discovered that he could have made a better deal.  The professor borrowed 10 Euros from his wife and repurchased the horse from his neighbor for 80 Euros, which he then sold to a different neighbor for 90 Euros.


How much money did Professor Egghead make through his transactions?

How Many Queens on a Chess Board?

Can you place eight Queens on a chess board so that no Queen can be 'taken' by any of the other Queens?

There are several unique solutions (ie. not reversals or rotations).  For an additional challenge, find all the solutions.

Mutab, Neda, and Sogal

Today's puzzle comes from an old copy of Best of Creative Computing, Volume 1.  In 1976, Walter Koetke, of Lexington High School presented the following:

If you think you've seen this problem before, you may be correct. It's a really old problem in a new disguise.

The civilizations of three planets Neda, Mutab, and Sogal have agreed to begin war in the year 2431. Although these societies have not eliminated such irrational actions as war, they have at least formalized the process. There are, for instance, no guerrilla activities and wars are usually very brief and always decisive. Wars are fought with inter-planetary rockets each of which is powerful enough to completely destroy an entire planet. With such powerful weapons at their disposal, Neda, Mutab, ad Sogal have agreed to the following set of rules, for only in this way can they be assured of a single victor.

Rule 1: The fight will continue until only one civilization remains.
Rule 2: The rather primitive technique of drawing lots will be used to determine which planet may launch the first rocket, which the second, and which the third.
Rule 3: After launching rotation is established, rocket launching begins and continues in order until only one planet remains.

When contemplating the outcome of this war, the three civilizations have full knowledge of the background of their adversaries.

Mutab is clearly the technologically superior civilization. Once launched, their rockets always strike with perfect accuracy - thus disproving a modern theory that nothing is perfect. Before the war begins, both of the other civilizations are aware of the terrifying fact that if a Mutab rocket is fired at them, the probability of their being completely destroyed is 1.

Neda is the oldest civilization and long ago had the superior technology. However, the complacency of a self-centered, unchallenged mind has been eroding this superiority for many years. As a result, the technology of Neda has not advanced in over 40 years. If a Nedian rocket is fired at another planet, the probability of hitting that planet is 0.8, just as it was 40 years ago.

Sogal is by far the newest of the three civilizations. Being dedicated to producing its own technology on its own terms has resulted in a proud and purposeful civilization, but one that is technologically four or five hundred years behind its present adversaries. A missile launched by Sogal has only a 50-50 chance of reaching its intended target.

Your role in this future war is to determine each civilization's probability of winning.

Restoration - Logic Puzzle

This logic puzzle comes from the August 2003 Number 2 edition of Superb Variety Puzzles Plus Crosswords from Kappa Publishing Group.


Alexis has recently bought a charming Victorian house. She plans to do various projects over the next few months (August through December) to restore the house to its intended state, and has enlisted a different friend (including Golda) to help her with each task. Discover the month in which she will do each project and the friend who will help.

1. Alexis needs to remove the acoustic drop ceilings sometime before she installs period lighting fixtures.
2. She needs to take up the shag carpeting sometime before she refinishes the wood floors underneath.
3. Harry hasn't been enlisted to assist the month before Natasha.
4. The people who help Alexis remove the carpeting and wall paneling aren't of the same sex.
5. A woman will help her install the lighting fixtures.
6. Alexis will receive help from Kyle three months after she removes the wall paneling.
7. A man will help her in December.
8. Jed will help Alexis either the month before or the month after she refinishes the wood floors.

There Once Was a Woman and She...

This riddle comes from Martin Gardner's book Aha! Gotcha.


Say the following couplet so that it rhymes:

     "There once was a woman and she
     was deaf as a post."



If you'd like to see more puzzles from Martin Gardner be sure to check out the following books:

Binary Primes

The non-blog version of The Puzzle Page has published a new binary crossnumber puzzle.  This is similar to another binary crossnumber puzzle posted on this blog earlier.

 

As with the previous puzzle, the object of this one is to fill the 16 squares with the appropriate binary numbers.  If you need a refresher on how decimal numbers compare to binary numbers DEW Associates Corporation has a very nice number conversion chart on their website.

 

 

Across
  1.  4 Across - 4 Down.
  2.  A multiple of 3.
  3.  Same as 1 Down.
  4.  A prime number.

Down
  1.  A prime number.
  2.  Twice the value of 3 Across.
  3.  4 Across - 2 Down.
  4.  A prime number.

Hint: The three prime numbers (4 Across, 1 Down, and 4 Down) are unique.

 

 

 

If you like crossnumber puzzles consider these books from Amazon:

• 40 Cross-Number Puzzles: Addition & Subtraction
• 40 Cross-number Puzzles: Multiplication & Division (40 Cros-number Puzzles)
• Crossnumber Puzzles: Boosting Skills to Meet Assessment Goals (Crossnumber Puzzles, Grade 6: Extended Skills)
• Crossnumber Puzzles: 50 Crossnumber Puzzles With Solution Guides And Solutions

Thirds and Differences

Here's a nice little problem that can be figured out using algebra or using a little guess-work and a bit of luck.  It should be suitable for older elementary school or high school students.

1  2  3  4  5  6  7  8  9

Arrange the digits 1-9 so that the first 3 form a number that is 1/3 of the number formed by the last three and the three digits in the middle form a number that is the difference between them.

The numbers are as they appear, not summed.


There are 362880 ways to arrange the nine digits and 4 valid solutions to this puzzle.  Good luck!

A Small Town Affair

Here's a puzzle that appeared in Creative Computing magazine back in 1974.

There is a small town of a few hundred inhabitants of which the following statements are surprisingly true:

1. Every man is a perfect logician and is aware that this is true of every other man in the town.
2. Every man in the town knows all about the behavior of every woman in the town, with the exception, if he is married, of his own wife. It is taboo for anyone to speak about a woman to her husband. 
3. It is an immutable custom (abhorrent to us maybe, but as inevitable as night following day to them) that, when a man discovers that his wife has been unfaithful, he takes her out into the town square that same night, and on the stroke of midnight shoots her. 
4. There are 40 unfaithful wives in town.

Now, life has been continuing its uneventful course for some time when, one fateful summer's day, June 1st actually, the Mayor summons all the townsmen to a meeting in the town hall. 'I am very sorry to have to tell you this,' he says, 'but there is an unfaithful wife in this town.' The meeting ends and the men disperse.

 

What, if anything, happens, and when? (NOT an easy problem.)



If you like these kinds of puzzles you may enjoy these:

Challenging Logic Puzzles (Mensa)

My Best Mathematical and Logic Puzzles (Math & Logic Puzzles)

 

Dropdown Puzzle 2

You can find the first Dropdown puzzle here.  Fill the empty squares in the bottom half using the letters in the respective columns in the top half to see a quote.  This type of crossword puzzle is also called a Quotefall, Dropline, or 'Fit the Quote' puzzle.

For a whole book filled with similar puzzles check out:  Quotefalls Volume 32, Selected Puzzles

Spam

Due to the high number of spam comments left by anonymous users, the ability to leave anonymous comments has been turned off temporarily.  You can still leave a comment by signing in with your Google or OpenID password.

When First the Marriage Knot was Ty'd

This little puzzle comes from a book honoring the great puzzle master Martin Gardner.  In the chapter titled Some Diophantine Recreations, David Singmaster presents the following poem which appeared in The American Tutor’s Assistant, in 1791.


When first the marriage knot was ty’d
Between my wife and me,
My age was to that of my bride
As three times three to three
But now when ten and half ten years,
We man and wife have been,
Her age to mine exactly bears,
As eight is to sixteen;
Now tell, I pray, from what I’ve said,

What were our ages when we wed?

Behind the Green Door

You are a captive in a far away land.  The king offers to set you free if you can pass the following test:

You are to be placed in a room with two doors.  Behind one door is a ferocious tiger, behind the other is your escape.  30 feet above each door is a window where a man is sitting.  One man always tells the truth, the other is an incessant liar.  You may ask only one question.

To ensure your safe passage, what should your question be?

An International Neighborhood

Five immigrant friends meet every Thursday to play poker. While they all live in the same neighborhood, each comes from a different country and each lives on a different street. They each favor a different beverage, keep a different kind of pet, have a different occupation, and each is a different age.

Use the following clues to see if you can find out who drinks the whiskey and who is the tailor.

1. The Italian drinks brandy.
2. The man who lives on Green St. has a canary.
3. The oldest man lives directly behind the grocer.
4. Western Ave. and Green St. run parallel to each other.
5. The Irish man's age is exactly between the oldest man and the Swede.
6. The man who drinks wine is 33 years old.
7. The man who lives on Main St. is exactly 11 years older than the cobbler.
8. The 38-year-old man keeps an iguana.
9. The man who has the dog is 6 years older than the man who has the fish.
10. The German is 55 years old.
11. The Russian lives directly behind the butcher.
12. The road the beer drinker lives on is perpendicular to the road the cat owner lives on.
13. The road the scotch drinker lives on crosses Elm St.
14. The baker lives on Main St.
15. The brandy drinker is 5 years older than the man who lives on Green St.
16. The youngest man lives on Elm St.
17. The age difference between the cat owner and the beer drinker is exactly the same as the age difference between the Italian and the man on Atlantic Avenue.
18. The age difference between the youngest and second to youngest is the same as the age difference between the man with the canary and the baker.
19. There is exactly 22 years difference between the youngest and oldest men.
20. The grocer drinks beer.

To help solve the puzzle, here is a map of the neighborhood showing where the houses of the five men are located.

A Strange Safari - Part 1

Professor Egghead went on a safari to Australia last January to see ostriches and dingoes. He called me up the day he arrived on the ranch to tell me what it was like. I asked him how many wild animals he had seen and he replied that he had only seen people and horses, but he didn't remember how many of each there were. He did remember, though, that between the people and horses there were 22 eyes and 34 legs.

How many humans and how many horses did the professor see?