EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find a great variety of ways of asking questions which make 8.
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
1) Can you draw a straight line across the
centre of a clock face so that the numbers on both sides of the
line have the same total? Can you do this another way?
Andy, Courtney, Lukas and others solved this
by looking at the sum of the numbers on the clock face, and then
trial and error. Lauren writes;
A group from Archers Court in Dover solved the
problem using an algebraic method. This method also helps the
second question, on whether there is another solution.
2) Can you draw two lines (like the hands of
the clock) to divide the clock face so that the total of the
numbers on one side of the lines is twice the total on the other
side? Can you do this in another way?
Junnrui Hu wrote;
3) Can you divide the clock face so that that
the total on one side of the lines is five times more than the
total on the other side? Can you do this in another way?
Harry from the Beacon School solved this using
an algebraic method.
4) Can you draw two lines to divide the
numbers so that the total of the numbers on each side of the lines
are both multiples of six? In how many different ways can you do
Lily and Amy from Bow Brickhill School solved
this problem using a method of trial and error, by adding consecutive numbers until they totaled a
multiple of $6$. They found that $9+10+11+12=42 (7\times 6),
1+2+3=6 (1\times 6), 4+5+6+7+8=30 (5\times 6)$. Here they have
found three groups that sum to a multiple of six, so any
combination of these will work, say having the lines after
$8$ and after $3$, or after $8$ and after $12$, or after $12$ and
Susanna from St George's also used a trial and
error method to find several solutions.
5) Can you draw two lines so that the numbers
on each side add to a prime number? Can you do this in another
Junnrui Hu answers this;
Well done to Junnrui Hu for his excellent
answers, attempting every single question. Congratulations also to
Ian who solved every question using just his knowledge of
triangular and prime numbers.
The last question remains open to anyone who
wishes to investigate it, can you find any other interesting ways
to group the numbers on a clock face by drawing two lines?