Stage: 4 Challenge Level:
Stephen from Framwellgate School sent us
his reasoning about this problem, which gives us one of the
It is easy to see that the word sheffuls needs to have the e (which
is in the third place) moved to the position the l (the seventh
place) is, which needs to go to where the u (the sixth place) is
and simply this u needs to go where the e was, so it can be
represented on the cycle (3 7 6)
Mr Skipper from Smithden High has extended
this to find all possible solutions:
The double f can stay where it is or switch around (making the
first f into the second and vice versa). So either (4)(5) or (4 5).
In the same way we have a choice with the first and second s. So
either (1)(8) or (1 8).
So the options are (omitting 1-cycles for readability)
(3 7 6)
(1 8) (3 7 6)
(3 7 6) (4 5)
(1 8) (3 7 6) (4 5)
These can be written in different ways e.g. the last one could be
written as (5 4) (6 3 7) (1 8), but this is effectively the same
reordering, just written differently.