Oscar Ropes Puzzle

We are done with the winter Olympics and now are looking forward to the Oscar's entertainment. 

As we saw in the previous puzzle, the most interesting stuff happens away from the main arena and escapes the media attention:)   And what do we have on the margins of the Oscar ceremony? VIP ropes and poles that guard the Red Carpet attendees, of course. 

This a puzzle about two poles, 5 feet high each, and a rope connecting these poles. The rope is 6 feet long and at its lowest point is 2 feet above the ground. The question is: how far away are those poles?

This puzzle came from my son's friend Adam. Thank you!

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon. 

The Good Soldier Schweik and valet's dead grandmother.

Have you heard of a Good Soldier Schweik? It is a fictional character created by a Czech writer Jaroslav Hasek in 1914 but still popular all around the world for his naive nature combined with the ability to survive in the face of adversity and absurd situations.

At some point in the book Schweik demonstrates such enthusiasm in serving the Emperor that his sanity is questioned and he appears before the medical board. He is asked by the certified psychologists:

"Is radium heavier than lead?"

"Please sir, I haven't weighed it," answered Schweik with his sweet smile.

"Do you believe in the end of the world?"

"I'd have to see that end first," Schweik answered nonchalantly. "But certainly I shan't see it tomorrow."

"Would you know how to calculate the diameter of the globe?"

"No, I'm afraid I wouldn't," answered Schweik , "but I'd like to ask you a riddle myself, gentlemen. Take a three-storied house, with eight windows on each floor. On the roof there are two dormer windows and two chimneys. On every floor there are two tenants. And now, tell me, gentlemen, in what year the valet's grandmother died?"

So, can you solve this Schweik's puzzle or you agree with the medical board that certified him as insane?

What if you were whispered another condition: the year that valet's grandmother died is equal to a product of a number of house windows by a number of house chimneys by the age of one of the tenants (age in the year 1914 when the book was written), tenant that was actually present at this funeral.  What year valet's grandmother died?

Submit your answer any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

This puzzle is from the Russian Journal Kvant.

The Sand Clock Puzzle

I recently bought an elegant sand clock and for a few days we were trying to figure out how long does it take for the sand to go all the way down.  Turns out it is around two hours but it appears to change with the room temperature and our lack of patience. Occasionally, sand particles get stuck in the narrow middle passage and then - the time stands still.  Like a globe, sand clock is a great home toy and reminiscence of our rich history.

Apparently sand clocks and water clocks came to replace the shadow (sun) clocks that couldn't work at night. The first water clock was created in Egypt by using a water bucket with a tiny hole in the bottom. As water dripped down, marks were placed on the bucket to mark hour intervals. Soon water clock design evolved into two buckets.  But water clocks had an unexpected flow - they couldn't be used on the ships. Motion of a ship pushed water all around the containers. Someone got an ingenious idea to replace water with sand and such sand clocks became indispensable the 14th century discovery voyages. Story tells that Magellan had 18 sand clocks per ship.

Why did he need more than one?  Perhaps they were of different sand volume and measured different time intervals. Here is a relevant puzzle. Assume Magellan's cook has two sand clocks that measure 7 and 11 minutes. Magellan's favorite fish takes exactly 15 min to be made according to his taste. How can the cook measure 15 min with a 7 and 11 min sand clocks?

Want to make a sand clock at home from two plastic bottles? See these video instructions.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon. 

Red Lights Puzzle

Does it ever happen to you - a week with no inspiration? Your baby is sick, your older kids are on vacation and require entertainment and it is very hot and humid outside. Well, this is my excuse for skipping last week's puzzle. But just as the week ended I went to see a movie with my husband, and here it was - a puzzle in a movie. The movie, Red Lights, is masterfully done and acted, and keeps you in a constant suspense. But then, just as you expect an original resolution, it flops and disappointingly ends leaving some ends loose.

You can skip the movie, but solve this movie's puzzle:

Robert DeNiro's character is a legendary blind psychic that agrees to be subjected to scientific tests verifying his paranormal capabilities. In one of the tests he has to guess random numbers picked up by an independent person behind the wall by reading his mind.  The person picks a number between 1 and 12 and signals the psychic that a number is chosen.  The psychic attempts to guess what number it is. Then the experiment repeated in the same manner.  The psychic was able to guess those numbers with a very high success rate, much higher than chance. Is he really capable of mind reading? When we and the scientists view experiment's videotapes we can see that psychic makes a key comment about his watch and asks scientists (that are inspecting the watch for fraud) to be very careful with its gentle hands. How can the watch be used by the psychic to fool everyone in this experiment without any obvious fraud?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Image by Artnow314, distributed under CCL.

Celebrity Age Puzzle

They are both in their twenties. She met him when he guest-starred in her episode shooting and turned out that the date happened to be simultaneously  his and hers birthday.  They have been inseparable since then. To the paparazzi's question about their ages he replied that he is four times as old as she was when he was three times as old as she was when he was twice as old as she was. What are their ages now?

Image by JND90745, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Kant's Clock

A famous old puzzle.

It is said that Immanuel Kant was a bachelor of such regular habits hat the people in his town would adjust their clocks when they saw him strolling past certain landmarks.

One evening Kant was dismayed to discover that his clock had run down.  Evidently, his servant had forgotten to wind it.  The  great philosopher did not reset his hands because his watch was being repaired and he had no way of knowing the correct time. He walked to the home of his friend Schmidt, a merchant who lived a mile or so away, glancing at the clock in Schmidt's hallway as he entered the house.

After visiting Schmidt for several hours Kant left and walked home along the route by which he came. As always he walked with a slow steady gait that had not varied in twenty years. He had no notion how long this trip took. Nevertheless, when Kant entered his house, he immediately set his clock correctly.

How did Kant know the correct time?

Top image by faungg, distributed under the CCL.

Answer ideas accepted any time until midnight on Saturday September 17th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

Life, in Fractions

Math is old. Diophantus of Alexandria (now Egypt, then under a Greek rule) who lived 18 centuries ago is frequently called the father of algebra or a satan of algebra. He wrote 13 books that he titled "Arithmetica" containing various numerical problems and their solutions.  Diophantus was the first Greek mathematician who recognized fractions as numbers. In a tribute to him one of his admirers described his life as a fraction riddle:

Diophantus' youth laster 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later he had a son. The son lived exactly 1/2 as long as his father, and Diophantus died just four years after his son's death. All of this totals the years Diophantus lived.

The question is whether all this info is enough to determine how long Diophantus lived? Prove it!

Top image by freeasfreedom, distributed under the CCL.

Answer ideas accepted any time until midnight on Saturday September 10th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

Is Lynnet Misleading Lady Gaga?

Stefani Germanotta (better known as Lady Gaga) was planning her post Grammy concert in New England. Her newly hired manager, the famous young math whiz named Lynnet did some statistical analysis and told Lady Gaga that in Boston, MA there are about 10,000 fans who are likely to attend her concert even if they need to drive for two hours, in Hartford, CT - 9,000 fans and in Providence, RI - 8,000 fans who are similarly so eager to see Gaga that they could drive almost anywhere in New England. Each of these cities have large concert halls capable to fit audience of up to 30,000. Distance between Boston and Providence is about 50 miles, Boston and Hartford is 100 miles and Hartford and Providence is approx. 80 miles. Lynnet and Lady Gaga met in the office and contemplated where to hold the concert in order to minimize the total amount of miles travelled by all the fans. Lady Gaga concluded: Ok, then Boston it is, as the city with the largest amount of fans. But Lynnet convinced her otherwise. How? And what city the concert is going to be?


Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

How long did he live?

Here is an ancient Greek puzzle about Diophantus, who is believed to be the father of algebra:
This tomb hold Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.

How long did Diophantus live?
Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Archimedes' Grave

Archimedes made a plenitude of significant scientific discoveries throughout his life. He designed machines capable of lifting attacking ships out of the water as well as mirror arrays capable of focusing sun rays and setting enemy ships on fire. He explained why and how bodies float in the water, helping the king verify that his crown is indeed made out of pure gold. He was fascinated with infinity and found the way of approximating the number Pi as well as counting the number of grains of sand that will fit inside the universe. He died telling a Roman soldier that he is too busy to meet a general as he was contemplating yet another mathematical diagram. His tomb was decorated with his favorite discovery .... What do you think it is? Explain why to get a puzzle point.

Who is tetractys?

Cast your votes below. Explain them in the comment section. Person who will provide the best explanation (and the correct one), will get a puzzle point.

Michelle Obama's Plane

Michelle Obama was returning from LA on a 747 and her White House Chief of Security planned to pick her at the airport in a special bulletproof car. Obama's plane landed ahead of schedule and the security chief unaware of it was still on his way. Michelle took a congressman's limousine back home. Fifteen minutes later security chief car intercepted the limousine on the way and asked the First Lady to switch cars. She was so happy to be back at the White House twenty minutes earlier than scheduled. When Washington chief of security had to file a day progress report, he was at loss as to when exactly the plane landed. The original schedule stated landing at 3.30pm. Can you help him?


This is a fictional story. The puzzle is adopted from the book by B. Kordemsky

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Oscar Math

Just one week after Shaun White, Linsdey Vonn and Evan Lysacek left our living rooms, Hollywood actors arrive in full glamor for a sparkling Oscar Ceremony.


This year, voting rules for the Best Movie have been changed and the results may be full of surprises. It used to be that the Best Movie category had five nominees and every member of the academy chose one. The movie that received the most votes was the winner. Now, you have to sit down just to listen to new rules, as your head may start spinning.
Ready?
This year there are ten nominees in the Best Movie category. Members of the academy rank nominees in order of preference. Judges sort all the ballots into ten piles based on the first place selection. If one movie gets more than 50% of all first-place votes: it is the winner. If not, then the movie that received the least amount of first-place votes is eliminated. Its ballots are then redistributed into the remaining piles according to the movie that is ranked second on each of these ballots. If those second-place votes are enough to push one of the other nominees over the 50% threshold, the count ends. If not, the smallest of the nine remaining piles is likewise redistributed. Then the smallest of the eight piles, then the smallest of the seven…

Can you devise a scenario when a movie favored least in the old counting system will be the winner this year?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Cleopatra's Milk Bath

Have you heard about the new spa treatment: Cleopatra's Milk Bath? This fresh milk bath takes just one hour, costs $100 and is suppose to cleanse and moisturize the skin. The treatment is inspired by the Egyptian queen Cleopatra that had a remarkable beauty and uniquely smooth and soft skin. It is believed that she was bathing in milk.


If it worked for Cleopatra, it surely should make magic for us. Shall you try a milk spa that runs $100 for an hour or create your own milk bath at home? How much milk would you need for such a bath assuming that you use 50% milk and 50% hot water? How expensive the homemade milk bath may be?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

White House Party Crashers

A couple from Virginia breezed through the White House security and leisurely enjoyed the State Dinner with the president, vice-president, Indian Prime Minister and an array of other hand-picked guests. All is well, except that the couple has not even been invited to this dinner... Wow!
How did they do it? Rumor has it that the secret service agent asked them "Have you been invited?" They answered: "Yes!" and walked right in. While the Secret Service is trying to figure out how they let it happen, I suggest we help them with some logic. Our world consists of liars and truth tellers. The liars got entangled in their lies so deeply that they always lie, and the truth tellers are always honest. Both, liars and truth tellers, are occasionally being invited to White House parties. And both, liars and truth tellers, may occasionally have an impulse to attempt to crash a White House party uninvited. What question you suggest Secret Service agents ask any party goer, in order to let through only those invited, be it a liar or a truth teller?



(this puzzle is inspired by Giovanni Ciriani's answer to one of our recent puzzles)

To get a correct answer point, please explain your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

The Lightbulb Puzzle

Here is a good old puzzle that was also featured in a recent Spanish thriller "Fermat's room". Characters had only one minute to solve this puzzle before room walls would smash then dead:

There is a sealed room containing one light bulb. Outside of the room there are three switches, only one of which operates the bulb. You can turn switches On and Off in any way you see it fit. How can you guess which switch operates the bulb in the room, if you could only open the door and look inside the room once?

To know more about "Fermat's Room" movie and other breathtaking Math Adventures, read this recent story from TheMathMom.

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Did You See the President's Speech?

President has addressed the students today and his speech was aired live to all 1,000 high school students in my town. Middle school students got assignment to watch the speech at home. 900 will do that. 50% of all the middle and high schoolers will excitedly share this with their parents and 30% of these parents will watch as well. 150 of the elementary schoolers will try to imitate their older siblings and will watch the speech as well. Assuming that everyone who watches will share some details with at least three people in town who did not see it, two of whom will watch it and spread the news to another three oblivious people, will every person school age and above (10,000 people) know about this speech by tomorrow?

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Pyongyang to LA

Bill Clinton just returned from Pyongyang (capital of North Korea), bringing back the two jailed journalists to their families in Burbank, California. For this trip across the Pacific, he borrowed a 737 from his friend, a film producer. How many countries did he have to negotiate with for the air space if the pilot took the shortest flight route?

A hint could be found in this story.

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Santa's helpers

Santa Claus found that two elves could pack two stockings in two minutes. How many temporary elves did Santa Claus have to hire to get those stockings packed at the rate of eighteen stockings every six minutes? (from the book by A. Salny)

Missing winter holidays? Try this musing from TheMathMom: Christmas Beauty Pageant