Professional circles
Problem
Six friends sat around a circular table. Ann (who is not the banker) sat opposite the consultant. Bob sat opposite Fred. Celia sat on the doctor's right. Dave (who is not the consultant) sat opposite the accountant. Emily sat opposite the engineer and next to the financier. Fred sat on Ann's right.
Who sat where and what were their professions? Is there more
than one solution?
(Thank you to John Webb of Cape Town University for this problem
and greetings to readers of the Mathematical Digest in South
Africa.)
Student Solutions
Wong Jing and Wan Paul, River Valley High School, found both solutions to this problem as did Anne from Madras College, St Andrews. One or other of the solutions was found by Maria, Madras College; Caroline, Sophie, Laura and Emma, The Mount School, York; Henry, New College School, Oxford; Prav, Sheli and Ruoyi, from North London Collegiate School Puzzle Club; Becky, Richard, Chris and Richard all from Bourne Grammar School; Ashley, Mansfield, Australia and Isobel and Lottie.
Six friends sat around a circular table. Ann (who is not the banker) sat opposite the consultant. Bob sat opposite Fred. Celia sat on the doctor's right. Dave (who is not the consultant) sat opposite the accountant. Emily sat opposite the engineer and next to the financier. Fred sat on Ann's right.
1 st solution
2 nd Solution
Teachers' Resources
Why do this problem
Possible approach
Key questions
In what ways could you record this problem?Would a picture help, or pieces of paper, or a table.....
Possible extension
Suggest that the children make up their own similar question.You may choose to restrict the number of seated friends to four in the first instance. Making up a question is not difficult - the challenging part is in deciding which information, and how much of it, to give to make the question solvable but not trivial.
Possible support
In order to incluide as many children as possble, you could have some additional clues available, which the children could choose to use if they need them.In this way all children do the same problembut with varying levels of support.