An Olympic Puzzle

February 2014. Russia, Sochi.
Taxi drivers in the city are very busy bouncing all the athletes and spectators in-between the Olympic village and the city. This is a puzzle about two taxis: say Green and Yellow. Green taxi starts from the village and goes toward the city exactly at the same time when Yellow taxi leaves the city in the direction of the village.  They drive toward each other and meet (for the first time) 5 km from the village. Each delivers its passengers and immediately returns back with the new riders: Green taxi now drives from the city to the village while Yellow taxi returns from the village to the city. They meet (for the second time) 3 km from the city.
The question is very simple - how far is the Olympic village from the city?
Here is the sketch created by Kimberly Rose that should help you.

Note that this puzzle is fictional and Googling the real distance will not provide the answer. The puzzle is adapted from a summer boat puzzle from my favorite book of puzzles:

 

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

There are two types of drivers

This puzzle celebrates our master puzzle solver: Bean.

A holiday table conversation at Bean's household this week was prompted by one of the guests getting stuck on the way to the dinner without gas, which led to musing about two types of drivers. There are those who prefer to live on a safe side, possibly because they have nightmarish memories (or nightmarish fantasies) of their car stopping in the worst place and at the worst time. They refill as soon as the gas meter is showing less than half a tank. And there are those drivers, like our expert puzzle solver Bean, who enjoy taking a bit of risk here and there, rationalizing that to get to know this world you need to explore its boundaries. They zip to the gas station only after the tank is 90% empty and the low gas light turns on.

Do you think that by taking some risk this second group of people can save some time and/or money?
Bean was arguing that she can save a few hours per year and enjoy an extra family movie by pushing refills from 40% full tank to 5% full tank. Is she right? Assume a 17 gallon tank that runs empty in exactly a week, and that it takes 7 min to stop at the gas station.

Top image by gypsygen, distributed under CCL.

Answers accepted all day long on Friday April 22nd and Saturday April 23rd, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

A Rare Walking Occasion

Let's assume that our great puzzle solver Tom is a showbiz pro as he hinted in the Lady Gaga's puzzle. In fact he is so famous and rich that he has a car with a private chauffeur and he rarely walks. Every day he takes a train home from work (let's say Fifth ave, Manhattan), and his train arrives at the station at the same time each day. His chauffeur drives the distance from Tom’s house to the station at a uniform rate, and times his arrival at the station to exactly meet Tom’s train. He picks Tom up and turns around in negligible time, and drives him home from the station.

One day rushing from work for a romantic dinner Tom catches an earlier train, and arrives at the station an hour earlier than usual. He was not able to notify the chauffeur of his early arrival. Trying to get home fast he starts walking home along the route the chauffeur takes, at a brisk rate of 3 miles per hour. When the chauffeur, going to meet the usual train, sees Tom walking, the chauffeur stops, picks up Tom, and quickly turns around. They arrive home 40 minutes earlier than they usually do.

At dinner time, Tom's date is surprised to hear that he actually walked to be ready on time and is curious how long was the distance that he covered by foot. Can you help Tom figure it out?

This puzzle was suggested by Lawrence K. It is featured in a few old math puzzle books.

Top image by Clodius Maximus, 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 reasonable will get a puzzle point. Please, explain your answer.

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.

What's wrong with your head?

A fun puzzle from my son's friend. Thank you, Elliot!

A man set out for a walk. At the end of his walk his head had travelled 40 feet farther than his feet had travelled. He was a healthy man with all his limbs intact before and after the walk. So how did his head travel farther than his feet?

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.

Image by darkpony. distributed under CCL.

New Tires: When Do You Need Them and Tricks You Should or Shouldn't Do With Them

If on a recent winter family vacation you car was screeching, barking and jumping like a scared small puppy (as our car) instead of smoothly gliding through little hills of the freshly pressed snow, you may need new tires.

We learned that a simple penny test can tell whether tires have been so brushed by use that they lost necessary friction. Ridges on the tire should be at least 1.6mm deep for a safe driving on a slippery surface. This means that if you place a penny in the tire ridges, you should not be able to see the tip of the Abraham Lincolns’ hair on the penny. The expected tire use is 6-10 years. It is usually recommended to replace all 4 tires at once.

Now, a puzzle:
Assume that you just bought four new tires for your car. Your car manual says that your front tires could last you 25,000 miles. Your back tires 15,000 miles. You are trying to be creative and come up with an idea of switching your front tires with your back tires after driving 10,000 miles. What tires will go bad now? When?

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.

Should you do this in a car?

Do you leave home in a rush in the morning and continue your beautification routine in the car? Do you floss, shave, pick your nose, put make-up or lipstick while driving assuming no one around will pay any attention? Well, sometimes... Then, this is a great puzzle for you:

Illustration by Mike Kline, distributed under CCL

If you can see a driver behind you in your car's rear view mirror, does it mean this driver can spy on your beautification routine? Please explain your answer.

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who provided a correct solution will get a puzzle point.

How Long is the Traffic Jam?

Image from Flickr

There was a giant traffic jam on I-95 yesterday. It seemed that 3 out of 6 lanes were closed and on the remaining lanes cars were driving with half the regular speed. Freeway was packed during the rush hours and people said that traffic jam continued for a few miles North. I am wondering whether someone has any suggestions on how to help police (and drivers) estimate the expected size of the traffic jam if they need to close half of a freeway in such a manner. What will happen if they close one lane? Two lanes? You can use your kids' computer games, real life examples, internet and real police help in your answers.

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

Left Turn on Red

I was driving today in downtown Boston where most of the streets are one-way and you find yourself going along rectangles of the streets again and again to find a parking spot. Like in an old computer game game.

A puzzle has startled me when I had to turn left and I am hoping you can help me figure it out. Imagine, that you are driving on a one-way street and you are turning left into another one-way street:


Can you turn left on red, from the leftmost lane, after stop? Why?

I felt unsure and decided not to risk turning. No one beeped from behind, seemingly agreeing with me. On the one hand, you would never turn left on red. But on the other hand, you could turn right on a red light in Massachusetts, if it is safe and unless a "No Turn On Red" signal is posted in front.


The left turn situation above is just a vertical flip of the right turn situation. If right turn is allowed, then left should also be.
What do you know?
What do you think?

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

Averaging the Speed

You decide to take your kids to a new fascinating movie experience: "Cloudy with a chance of meatballs" in 3D. Rushing to get to the theater in time you speed at 50mph on a 35mph road. On the way back you are trying to demonstrate to your kids that you are driving according to the law "on average" and therefore you go very slowly, at 25mph. Will your average speed be lawful?

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

If you can't see my mirrors, I can't see you.

Returning from a weekend in Maine, I noticed a truck on the highway with the following sticker on the back:


Do you think this statement true and why it may or may not be so?

This story contains a hint. Read it to see why you should not be nose picking while driving.

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

Wedding Planner

You are a wedding planner and you are scheduled to arrive at the wedding in another town at 6pm. From your past experience, you know that if you travel at 80 miles per hour, you would reach the town at 5pm, one hour earlier. If you travel at speed of 40 miles per hour, you would arrive at 7pm, an hour late. How fast should you travel to arrive precisely at 6pm and how far is this town?

Tire swap

Your just bought four new tires for your car. Your car manual says that your front tires could last you 25,000 miles. Your back tires 15,000 miles. You are trying to be creative and come up with an idea of switching your front tires with your back tires after driving 10,000 miles. What tires will go bad now? When?