As a math teacher, I always love to see folks doing real math on television. Last week, on The Amazing Race Canada (Season 3, Episode 7), there was a 'tricky' mathematical challenge. Contestants were given a list of Air Canada flights and asked to create a flight plan using Air Canada destinations from around the world. They had to find a set of flights that had a total flight time of 25 hours (or 1500 minutes). They also had to ensure they used "a combination of routes that travel to at least three continents". Calculating the flight time was the first hurdle. Since arrival and departures are listed in local time and the vast majority of these flights crossed multiple time zones, contestants had to use the universal time code for each city to correct for time changes. A number of teams were confused right from the start (there was a lot of fixed mindset talk from the contestants). One team used an 'Express Pass' to skip this challenge while two other teams gave up and took a 2 hour time penalty instead of continuing with the challenge, That is a lot of flights! There are 12 flights listed on the Europe board, 11 flights on the Asia Pacific board and 15 flights on The Americas board. If we use just one flight from each board (so that we visit three continents), there are a total of 1980 combinations (12*11*15=1980). The rules state that we have to visit at least three continents but it doesn't say how many flight to use so we could have a flight plan with more than three flights. If we add one additional flight to make a flight plan with four flights, now we have 69300 possible flight plans (12*11*15*35=69300... one flight from each board and any one of the remaining 35 flights). That is a LOT of trial and error. The two solutions shown on the episode contained 4 flights. Are there any 3 flight plans that would work? Here is what I did.
First I got some screen captures of the flight boards so I could read all the flight times. Then I put them all into an Excel spreadsheet to calculate the flight times in minutes. Next I played with Excel for about an hour to try to find an efficient way to calculate all the combinations of flights that I wanted to try and then gave up. Instead, I created a quick program in Python to calculate all the possible sets with just three flight plans. This turned out to be much easier than using Excel (just 8 lines of code). AList=[924,731,635,1016,802,640,831,744,767,658,772] BList=[566,453,488,408,447,433,424,461,457,490,522,514] CList=[343,87,99,192,325,616,324,363,650,335,337,77,183,640,316] for i in AList: for j in BList: for k in CList: if i+j+k==1500: print 'Eureka!',i,j,k Now, assuming that I calculated the correct flight times in my Excel spreadsheet, this gave me three possible solutions: 1 AC025 Vancouver to Shanghai, AC824 Toronto to Amsterdam, AC541 Toronto to Seattle 731 + 453 + 361 = 1500 minutes 2 AC084 Toronto to Tel Aviv, AC898 Edmonton to London, AC962 Toronto to Bogota 635 + 522 + 343 = 1500 minutes 3 AC056 Toronto to Dubai, AC1904 Toronto to Edinburgh, AC1973 Halifax to Calgary 767 + 408 +325 = 1500 minutes The two solutions that were shown on the episode using four flights are below: AC480 Toronto to Montreal, AC918 Toronto to Miamai, AC882 Toronto to Copenhagen, AC007 Vancouver to Hong Kong 77 + 192 + 447 + 784 = 1500 minutes AC230 Vancouver to Calgary, AC541 Vancouver to Seattle, AC1910 Montreal to Nice, AC009 Calgary to Tokyo 87 + 316 + 457 + 640 = 1500 minutes
There was a nice article posted online that interviewed the Air Canada captain that handed out the clue cards for the challenge. He mentions the factors that he said made this such a challenging competition.
EL
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