We received good solutions from Gareth, Ed and
Omer from Dartford Grammar School, Harry from Culford School and
Alex, Alice, George, Nell and Tom from Gorseland School. Thank you
Harry explained how he knows when it is his
turn to ring:
An easy way to remember when to ring is to notice a pattern.
e.g. 1, 1, 2, 3, 4, 4, 3, 2, 1, 1 is the exact pattern that bell 1
Your turn is first, then first again, then second, then third, and
so on (in each set of four).
After every ring, bell 1 initially rises up further to the
For bell 1 the pattern is: same, more, more, more, same and so on.
For bell 2 the pattern is: same, less, same, more, more, and so on.
For bell 3 the pattern is: same, more, same, less, less and so on.
For bell 4 the pattern is: same, less, less, less, same and so on.
From these data an easy pattern to remember for bell 1 is 1, 1, 2,
3, 4, 4, 3, 2, 1, 1, 2, 3, 4...
Alex, Alice, George, Nell and Tom from
Gorseland School sent the following explanation:
There is a certain pattern each bell follows.
Bell 1 rings first on the first sequence of four rings, second on
the second sequence, third on the third sequence and fourth on the
Then, on the fifth sequence, the bell rings fourth again, there
being four bells.
On the sixth, Bell 1 rings third again, second on the seventh
sequence, first on the eighth sequence, first on the ninth
sequence, second on the tenth sequence, and so on.
Each bell follows this pattern but starts in a different
Ken, a volunteer (and bellringer) helping at
their school wrote:
After half an hour of intense discussion about the problem, and the
various ways they might solve it, one of the children asked "Are we
not doing any maths this morning?"
They then wanted to stay in during break to see if they could
actually ring the bells - and did so quite well.
We are delighted you enjoyed the problem.