A blog about Mathematics and Mathematics Education in Singapore, as well as Mathematics Education in general. Written for students, parents, educators and other stakeholders in Singapore, and around the world.
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Sunday, May 24, 2015
[Pri20150523WNCA] Trees arranged in a Hexagon Outline
This is real eeeasy peasy lemon squeezy, isn’t it?
54 ¸ 6 = 9 Ta da!
The answer, right? Wrong! You got
tricked! Ha! Ha!
You can see
that the corner trees (coloured in orange instead of brown) are counted twice,
because they each serve as an extreme marker of two of the sides of the
hexagon. There are 18 trees and if you
divide by 6, you get
3 and not 4. One
way to count properly is to start from one corner tree and count groups of three
trees, either in a clockwise or anti-clockwise (American: counter-clockwise) direction.
the number of trees on one edge of the hexagon is equal to the number of trees in
one group plus one (the corner tree for the next group). So for
18 trees, the correct calculation
is 18 ¸ 6 + 1 = 3 + 1 = 4
for the number of trees along one edge.
We use the same procedure for
number of trees on each side = 54 ¸ 6 + 1 = 9 + 1 = 10
want to generalise it into a formula
# trees on each side = total # trees ¸ #sides + 1
However, I do not recommend that you purposely
memorise this formula. Mathematics is
not about memorisation. It is about
understanding. Once you understand it,
the formula comes out automatically. You
may test yourself or get a friend to test your understanding by setting a
similar question but changing the number of trees and number of sides.