Senior Challenge 6
To open a pdf version of this challenge for printing, please
click on the link below.
Senior
Challenge 6.pdf
Question 2 for this challenge continues the 'make
something fly' theme for
this semester. We made a test glooder with quite a light A4 sheet of
card - if the card is too heavy it won't make a ring very easily. As I'm
sure you know, MacDonalds have the best straws around (or used to when I
was a parent of young children). We actually used a lightweight coloured
stick of the type that is found in the DIY section of a Variety Store,
but I'm sure that a strong straw would do just as well.
Question 1
The positive whole numbers
5, 3, 4, 8, …
form the beginning of a naturally mathematical sequence
in which:
none of the numbers in the sequence are repeated
the sum of the first 2 numbers is divisible by 2,
the sum of the first 3 numbers is divisible by 3,
the sum of the first 4 numbers is divisible by 4,
and so on.
Construct a naturally mathematical sequence of 9
numbers.
By carefully choosing the numbers, how small can you
make the largest number in a naturally mathematical sequence of 9 numbers? |
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Question 2
How to make a Glooder
A glooder is a glider made with two rings of card and a
drinking straw. The rings are made by taping a thin rectangle into a
cylinder and leaving a small gap into which a straw is glued. There is one
ring at either end of the straw.
The rings should be 4cm wide for the large ring and 3cm
wide for the small ring, but we would like you to suggest a suitable ring
diameter for the large and small rings.
Questions
- Should you launch the glooder with the smaller ring
at the front or at the back?
- How large should the ring diameters be for best
flight results?
- Is this a ratio that works for a shorter glooder too?
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Question 3
We set out a row of counters numbered 1, 2, 3, and so
on. Our aim is to reverse the order of them but there is a special rule
for moving the counters.
Rule: You can move two adjacent counters to either the
beginning or the end of the row and then close the gap. For example:
With this rule:
- What is the least number of moves required to reverse
a row of four counters? If you double click the diagram, you can open
up an applet that will help you with this one.
- What is the least number of moves required to reverse
a row of five counters?
- It is not possible to reverse a row of six counters.
Why is this so?
- In general terms, what can you say about the length
of row that can be reversed?
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