Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
This investigation explores using different shapes as the hands of
the clock. What things occur as the the hands move.
Do you know the rhyme about ten green bottles hanging on a wall? If
the first bottle fell at ten past five and the others fell down at
5 minute intervals, what time would the last bottle fall down?
This was not only a first but also definitely a question for
Mondays! So, when did July 1st fall on a Monday again, or April
1st, or September 1st or even November 1st?
Robert, Keiichi and
Thomas , pupils at Moorfield Junior School, wrote that
they solved the questions posed by trial and error. This is what
they discovered for when July 1st falls over the next few
So, is the answer that, in the year 2013, July 1st will again be
on a Monday. Quite a wait! How old will you be then?
Jingjing are pupils from Kilvington Girls' Grammar School
which is in Melbourne, in the state of Victoria in Australia,
arrived at these answers for the other months:
Monday 1st Sept: 2008
Monday 1st Nov: 2010
Monday 1st April: 2013
Jade and Sarah , from
Newland Primary School made a list to help them organise the
information they needed to answer this problem. "This is how we
worked it out", they write:
So, the answer is 2007. But for which month?
Not sure? If you see how solutions are arrived at, it really
helps. Perhaps, this chart from Georgia (who lives in Suffolk in
England) might help you decide.
When you solve problems like this, try to see if there is a
pattern in the answers. That will help you find the next answer you
need. This is precisely what Kate did.
Kate provided a
description of how finding a pattern helped her solve this problem
and the thinking that was involved. Kate thinks she has clearly
proven that her answer is correct. Read through and see if you
agree with her.
If the date you are starting from is 3 years after a leap year,
this will mean it is 5 years before the same date on the same day
comes around again.
However, it the date is 2 years after a leap year, then it will
mean 11 years before the same day on the same date comes around
1 year after a leap year will mean that it is 6 years before the
same day comes again on the same date.
But, in a leap year there will be 6 years before the same day
comes again on the same date.
A pattern occurs starting with July 1st 2002 (2 years before a
leap year) 11, 6, 5, 6 and then back to 11. The same pattern occurs
with a different starting point, depending where you start in
relation to a leap year happening.
The numbers in each of the rows add to 28 years. So, there will
be four of the same day on the same date in every group of 28
years. As there are 7 days in a week and 4 full weeks in a month
and 7 x 4 = 28, this proves that my answer is right.
Now, who is going to argue with that!!
Thank you to all readers, including Tim , who sent in solutions to this