Bermuda Triangle Puzzle

I should warn you that this is a tricky one.  It came via Facebook and god knows what devil invented it but as all the good puzzles it is carefully retold through generations and social networks.

Two triangles consist of exactly the same shapes. Shaped are rearranged in a different order in the bottom triangle and suddenly... one square disappears. How did this "Bermuda Triangle" swallowed the square?

Fill free to print the pictures and play with them, use a ruler. Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon. You can also email me your drawings to maria@themathmom.com

Why don't they flip?

You have seen them in DC, Philadelphia, Vancouver or other places around the world - cool sculptures that seem out of balance; sculptures that appear on the verge of falling yet are perfectly stable.
How is it possible?
I know this is not really math but semi-related.

HaBima square, Israel

Laguna Beach, CA, USA

Norway

England

Philadelphia, PA, USA

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

Skiing Puzzle

A very cute puzzle from a great book by Ian Stewart "Professor Stewart's Cabinet of Mathematical Curiosities."

The little known village of Apres-le-Ski is situated in a deep mountain valley with vertical cliffs on both sides. The cliffs are 600 meters high on one side and 400 meters high on the other. A cable car runs from the foot of each cliff to the top of the other cliff, and the cables are perfectly straight. At what height above the ground do the two cables cross?  To make your explanations easier I marked with "h" the height we are looking for and with "a" and "b" parts of the base that you may want to use in your calculations. Remember that "h", "a" and "b" are all unknowns and we want the answer for "h" as a number.

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

Why things are not as they appear to be?

You are likely familiar with this sign on the side-view mirrors of some cars: "Objects in the mirror are closer than they appear." 

There are so many signs and instructions in the car that you probably avoid wondering about them up until your kids with their natural curiosity ask you: WHY? Let's try to run ahead of this question and figure out this WHY?

Why and how do you think these side-view mirrors distort reality?

 Image by Pratheep P S, www.pratheep.com, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday Janury 15th(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Lost Boarding Pass and Your Destiny

Many of us are traveling this Holiday time, visiting family and friends or running away from them to the mountains or remote islands. Chances are you may be reading this puzzle in the airport. Hold on tightly to your boarding pass.

In this famous puzzle adapted from Peter Winkler's book, we imagine ourselves boarding Aloha airlines airplane from Honolulu to Maui. Everyone is relaxed and happy. The first person that ascends the stairs to the plane holds his boarding pass in in his lips as both of his hands are holding two puppy cages. He smiles to the flight attendant, letting the boarding pass twirl down through the stairs and under the plane. He hesitates for a moment but then decides to perches himself into a random seat. Every next person goes to his or her assigned seat, but those who find their seat occupied politely avoid the argument by taking any random free seat on this short flight. You are the last passenger to board this fully packed 100-passenger plane. The problem is that you pleaded the Aloha ticket counter person to seat you next to this gorgeous surfer and now no longer sure both of you will get your assigned seats. What are the chances?

Image by rantingfan, distributed under CCL

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 sensible will get a puzzle point.

Airport Games

Imagine that you are stuck in the Newark Airport because of a silly security breach or thunderstorms and you are going out of your way keeping your kids awake and entertained for a few extra hours. Their favorite thing to do is go back and forth on the moving walkway. Your daughter is daring you to a race. She says: "Let's see who is faster: you going ALONGSIDE the walkway all the way to the end and then coming back, or me going ON the moving walkway first time in the direction of the motion and then back, against the direction of the motion. I will try to keep the same speed both ways." You are tired and frustrated because of the delay, but you are a parent. So, you agree. Who do you think is going to win?

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

Bullfight in Barcelona

This puzzle is rated PG-13 and touches a controversial issue.
We all heard about the Spanish tradition of bull fighting and have suspected it is still being practiced somewhere around the globe. Have you ever assumed you would witness one yourself?
Walking around Barcelona, my husband and I came to an intriguing castle that turned out to be Plaza de Toros Monumental, a bull fighting arena. We were fascinated to learn that it so happens that a rare bull fighting show is being held on the evening of the same day. Now, we strictly oppose animal cruelty. I stopped buying any leather or fur coats many years ago. My husband attempted vegetarianism but eventually we put a line at eating meat only once a week. Still, watching Corrida - Spanish bull fighting show - looked like once-in-a-lifetime-experience. It would happen with or without us. So, perhaps it is worth experiencing it. We bought the tickets, changed our plans and ambivalent about our actions, arrived to Plaza De Toros at 7.30pm.
It was a show: well-staged, acted, but disgusting and morally terrifying. In an hour during which our curiosity overstretched our guts, we saw four bulls masterfully killed right in front of our eyes. One was given a "parole" by the cheering crowd and the Presidente who looked like Don Corleone presiding over the show. I assume that at least two more bulls were killed after we left before the show was over. Six total.
I won't share the barbaric details of the process. It seems like this tradition is going away in Catalonia and perhaps in the rest of Spain. By observing it once most will alter their perception of Carmen's toreador and remove the imaginary veil of romanticism and heroism from bull fighting.
Apparently half of the meat from the killed bulls is donated to the poor and the rest is being sold to the restaurants around the town. Among the guilty nightmarish thoughts that occurred to me after the show was: what are the chances that we'll be eating meat from one of these six bulls served for dinner tomorrow? According to a recent survey, there are around 11,000 restaurants, bars and cafes in Barcelona. Say, each bull weights around 1,000 pounds. Assume that each meat portion is around half a pound. Dare to answer?

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The best deal on a plane ticket

Summer is a time of vacations and many of us have been or will be purchasing plane tickets for these long-dreamed-about trips. I usually look for a minimum number of stops, convenient hours, not too short and not too long a layover, and a familiar airline. Then, I go for the cheapest selection on this list. The difference between the least expensive choice and the next one is usually around 5%. That can be $50 for an International flight or $15 for domestic. Sounds like a good strategy, right? On my recent trip I was not so sure about that.
My least expensive choice didn't have personal TV screens in front of every seat, something that became very common on large planes and long international flights. On the way back, audio, light and even flight attendant buttons didn't work for the whole row of seats I was in. Toilets were dirty, food bad, flight attendants not very courteous. There were no eye cover and comfy socks that I know are being offered (or have been a year ago) on the airline that was next in price. Long-distance flights are never easy but for parents-flying-solo they can be rejuvenating: read, eat, watch, chat and sleep. Just yourself to worry about for a few hours or perhaps even a whole day. Quantifying all the things I expected but didn't get on my last trip, I am wondering whether this $50 difference was significant.

Perhaps I should adopt the same strategy as in a restaurant wine selection rule: pick second from the least expensive and you won't miss. What do you think?

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How long is the Loch Ness monster? - a tribute to M.Gardner

The Loch Ness monster's length is 20 meters plus half of its length. What is his total length?

This puzzle is from the Martin Gardner's "Aha!" book.
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When More is Less

I can not believe that I made the same mistake twice! My friend really likes the one particular brand of European hand cream and I have always been bringing this cream for her from abroad. I buy it at the Duty Free shop, put in my hand luggage and bring with me to the US. Usually there is a larger tube (150 ml) with extra 50% of this cream being free. And sometimes there is a set of three of such creams for the price of two at the Duty Free store.

I always go for the best deal. This unfortunately, did not do any good in the last two trips. Both times my trips included a stop-over, where my present-intended hand cream has been appropriated by the airport security as being above the allowed 100 ml amount. I wished I could give these free 50% extra back, turning the tube into a 100 ml volume. I blamed myself for being greedy, for forgetting about the new hand luggage rules, for not thinking forward. I blamed airport security and the Duty Free store. And still, year after year, in the frenzy and excitement of air travel, DutyFree shopping and enticing sale offers, I have been making the same mistake again... Going for more, I was left with less, or more precisely - no cream at all.

Enter your own story where More turns out to be Less on our Family Puzzle Marathon page. Be first to solve three puzzles and get a prize!

Cape Cod Puzzle

Summer on Cape Cod. Strong Wellfleet tides with water rising 3 inches per hour in the late afternoon. A fishing boat is unloading the Wellfleet oysters at the long deck. Rope ladder with 10 rungs is hanging over the side of the boat. The distance between each rung is 12 inches. The lowest rung is touching the water. How soon will the tide cover the third rung from the top of the rope ladder? (this puzzle was Massachusetts-ized from the book of B. Kordemsky)

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

In a hurry to unpack?

I was so happy when all our four suitcases got lost on a return from vacation. No hurry to unpack, shelve or wash all the clothes. We can first take care of the accumulated bills, holiday greeting cards and catalogs, settle back into our lives, deal with the jet lag and then... as in all the previous cases, suitcases will surface up in a few weeks. But all four of them surprisingly showed up on our doorsteps the morning after we arrived.

What shall I do? Unpack one every day; take a day off or wait till the weekend and and unpack all of them at once; unpack stuff as we need it - one item at a time; or unpack more and more every day as the jet lag slowly disappears and I can keep myself awake later.

Hokey Pokey Around the Globe

You take a mile hike South, then take a mile hike East, end with a mile hike North and find yourself at the starting spot. Where could you be on the globe? There are at least two answers.

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

Mess at the Marrakesh Market

Three boxes of fruit have been mislabeled at the Marrakesh Market. One box contains just apples, one contains just oranges, and one contains a mixture of both. However, instead of the correct labels "apples", "oranges", and "apples and oranges," wrong English label was placed on each box. How can you re-label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?

(this puzzle is adapted from the book "World's Best Logic Puzzles" by Seven Treasures Publication.)

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

Vegas or Egypt?

Imagine that you have been captured by a UFO, and after some time deposited back to earth. You open your eyes and see the sun straight above you, a palm tree, and a big stone sphinx in a sand. How do you know whether you are in Las Vegas or in Egypt?


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

Next Travel Destination

I love playing this game with the kids. We spin the globe fast. One of us closes his/her eyes and places the pointer finger on a spinning globe. We pretend that the point on a globe where the finger will be when the globe stops will define our next travel destination. Of course we couldn't afford to travel as much and as far as we spin the globe, but imagination takes us places. What happens to be our most frequent pretend travel destination?

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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!

Alin and Motti's Sunday Trip

One Sunday, Alin (the greatest puzzle solver of all times) and his friend Motti decided to go for a ride in the countryside. One rode a bicycle and the other a motorcycle. Sometime into their trip, a storm started and both had to call Motti's grandma to come to the rescue. When grandma came to pick up Motti, she noted that if he had ridden three times as far as he had, he would be two times as far to the start as he is to the finish. When she picked up Alin, she noted that if he had ridden half as far as he had, he would have three times as far to ride as he had.
Who rode the motorcycle?

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

Train Schedule

Two friends are traveling on a train from NY to Boston. One of the friends says "It seems that the Boston-NY trains pass us every 30 mins. How many Boston trains do you think arrive in NY every hour?"

Bear Attack

A man is stalking a bear that has attacked his camp. He reports later that naturally he went south. What color was the bear?