Today’s puzzle is a seasonal update of a cherished gem of British culture: the river-crossing puzzle, in which people travel back-and forth across a stretch of water in a very small vessel. The earliest-known river-crossing puzzles appear in a manuscript by Alcuin of York in the eighth century.
Another British cultural artefact from a distant age is the Carry On film. Not wanting to appear too parochial, however, today’s puzzle also includes an element from the Thousand and One Nights.
Six friends – Babs, Charles, Hattie, Joan, Kenneth and Sid – are going camping in France.
They are travelling across the Channel on a magic carpet (of course) that can take only two people at a time. So, in order for everyone to get across there will need to be 9 trips in total from their starting point in England: 5 across carrying two people, and 4 returning carrying one person. (Magic carpets cannot fly with no one on board, which is why one person needs to travel back. All the friends are able to fly alone on the carpet if need be.)
The faster the carpet flies, the bumpier the ride. Babs can fly at a speed that gets her to France in 1 minute. Charles feels queasy at that speed: his maximum speed gets him to France in 5 minutes. The others can get to France without suffering debilitating travel sickness no faster than 6 mins (Hattie), 7 mins (Joan), 8 mins (Kenneth) and 12 mins (Sid).
1. What is the least amount of flying time, in minutes, required to get everyone from England to France without anyone suffering from queasiness? (When two people are on the carpet together, the crossing will take as long as it takes the slowest of the two.)
2. Let’s say that the friends’ tolerance for travel-sickness means that their fastest journeys take the following times: Babs (1 minute), Charles (3 mins), Hattie (7 mins), Joan (9 mins), Kenneth (11 mins) and Sid (13 mins).
Now what is the least time, in minutes, required to fly all friends to France?
Here’s a tip: the answer to question 1 is less than 45 minutes. And the answer to question 2 is less than the answer to 1.
I’ll be back at 5pm UK time with the solutions.
Today’s problem is adapted from a question in the Computational and Algorithmic Thinking (CAT) competition, an event organised by the Australian Maths Trust in order to promote lateral thinking and problem solving, and unearth talent in computer programming. Today’s problem, by David Kennedy of the Anglican Church Grammar School, Brisbane, and Dr David Clark, chair of the CAT committee, appeared in the 2012 CAT.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of several book of puzzles and popular maths. If you are looking for something to distract your children over August, you might be interested in Football School: the Ultimate Puzzle Book, which has number games, word problems, riddles, lateral thinking and logic puzzles for 8 to 14-year-olds.