The Man Who Walked Between The Towers

You have probably heard about the daredevil Philippe Petit who sneaked on top of the World Trade Center and walked between the towers on a tightrope in  the August of 1974. I learned about him from a wonderful picture book by Mordecai Gerstein: The man who walked between the towers.  Here is one of the illustrations:

Some of you also likely saw the documentary made about Philippe Petit: Man on Wire and the animated film based on the above book.

A book, a documentary, an animation. Now it is time for a puzzle.

When Philippe Petit stepped onto the tightrope it was horizontally stretched between the towers. Under his weight, the cable hang a bit down. When Philippe reached the midpoint, the cable under his feet was 10 feet below its original horizontal position and the overall length of the cable got extended by 1 foot. What is the original length of the cable between the towers?

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

Swapping the Roles

Here is a trick that works great in coaching - whether for a math test, spelling test or almost anything else.  Ask your kid to be the teacher and give you the exercises that she/he think are going to be on the test. The hardest ones. While you will be playing a role of a student that solves the test but makes some mistakes. Let your kid check your test and find these mistakes.  Also, let her/him grade you.  Spice it up by playing misbehaving kids, excelling kids, failing kids. This is usually much more fun for them than the regular way of test prep.

I tried this with my daughter this week in preparation for her multiplication test. 20 multiplication exercises. I could solve only half... She liked it so much that next day she prepared a test sheet for me in advance at school and an answer sheet for her to grade me.

Now, let's try doing something similar with our puzzle today. Here is the story. Find what's wrong with it.

You want to send your kids to an 8-week long sleep away summer camp. But you don't have the $1,997 that it costs. How about asking for help from the grandparents? Each couple offers to give $1,000 toward the camp. You get the $2,000, pay for the camp and receive a $3 change. As a gesture you want to give each of the set of grandparents a $1 of change, and you keep a $1 for yourself as $3 is not divisible by 2.  So, now you owe each couple of grandparents $999, together you owe them $1,998. And you have $1 in your hands.  As you started with $2,000, this means that $1 + $1,998 = $2,000.  Right?

Disclosure: this puzzle is reinterpretation of a famous missing dollar puzzle that we discussed long time ago.

Dollar image from Flickr, distributed under CCL. Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

How Tall is Your House?

Imagine that you are shopping for a house and a Real Estate agent takes you to an amazing contemporary that looks something like this:

You inspect the house and climb up on top of the roof. You would like to know how tall the house is because a new law allows owners in this area to add another floor if the height of the house is below 10 meters. Unfortunately, blueprints with the specified height couldn't be found. Are there any experiments you can do to measure the height of the house? There may be more than one answer.

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

Pastry Dilemma

I was buying birthday pastry this week and saw that the 11" x 3" lemon pie is $24 while the 4" diameter round version of this pie is $10. And you know what is the best part of those pies? The buttery crust perimeter that is touching the delicious tart lemon filling and heavenly soft meringue.  If you want to spend $50 on the pies and would like to have the maximum perimeter-to-cake size ratio, what pies should you pick?

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.

The Pyramid Curse

A few months ago my daughter received a letter from a friend that invited her to join a mail game. You buy a sheet of stickers and mail it to the first address on the list. You then copy the list, removing the first address and shifting the rest, adding yours as fifths at the end. Then you mail this list with instructions to 5 of your friends. Wait a few weeks and then expect hundreds if not thousands of stickers by mail.
5^5=3,125
Sounds mathematically correct.

Such examples of pyramid behavior are everywhere:

1. an avalanche
2. a viral email with good jokes, scary health advisory, slides of the weird asphalt painting, gorgeous sunsets (that by-the-way never comes to your email box once)

Getting back to the Pyramid games, such as the sticker game my daughter received.  We all tried it at some point in our lives and were surprised to find out that they usually do not work. While one math reason makes them attractive, another math reason prevents them from running smoothly. What is it?

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

Sport Puzzles

Sorry, no puzzle or newsletter last week. My days have been very busy with the Holidays, vacation, taxes and my kids' birthdays. For those who haven't read about my April family management miscalculations, here is my Due Date Math story.

This week I am coming back with a set of sport puzzles. You can answer one or all in a single comment below.

1. By non-obvious reasons I seem to be taking to the sports my kids learn. Perhaps I am envious and want to be more than a driver, perhaps it is watching them play that sparks the idea, perhaps it is just a convenience.  So, in parallel with my daughter, I started taking group tennis lessons. There are four of us in the group. A few weeks ago one of the players didn't come and we all found ourselves much more exhausted than usual. No wonder, we each had to work harder. By how much?
2. During the tennis lesson we spend 50% of the time learning to play and 50% gathering tennis balls all around the court. We are all beginners and balls are spread all around the court, frequently all around the town. Each of us picks a quarter of the court and gather all the balls onto his/her racket. Usually one holds the racket flat in one hand and picks the balls with another, carefully managing the balance of the racket as it is filled with balls. I have been thinking that a different approach is easier and faster. Place the racket on the floor in the center of the ball cluster and pick balls with both hands, filling the racket. Then move the racket to another cluster. What do you think?
3. My father is jogging every morning. He runs a few mins and then walks the same number of mins, then runs again etc. His running speed is twice than his walking speed. When he started his jog the other day he met an old friend running with a slower speed than my father. They waved. After completing one run and walk cycle my father met this friend again. What can be said about their relative speeds?
4. My friend's kids went to the sports camp during their school vacation. Camp instructions say that everyone should wear red on Monday, yellow on Tuesday, green on Wednesday, blue on Thursday and black on Friday. On one of the days 1/3 of the kids came in rainbow shirts as they were not able to find clothes of the required color in their closet. What day was it?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.
Top image by Brooks Elliott, distributed under the CCL.