STRIPS

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STRIPS
By Emma Julia
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Question
Make a strip of squares. Colour some whole
squares black, leaving the others white.
Investigate!
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Using both Colour and Black and White.
All Coloured Squares.
What Colours Used? Red Blue Yellow.
What If?
All Black? All White?
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WHAT THAAAAAAA?!?!?!
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Where to Start?

• Paper and pen.
• A lot of Drawing and counting.
• A lot of confusion.

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Theory 1
That the number of combinations went up by 2 each
time.
2
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As you can see Theory 1 was disproved on the
third step.
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Theory 2
Our next thought was that perhaps this was a
pattern where by it went up by 2 then 3 then 4
then 5 then 6 and so on and so on and so on.
2 3 4
However on the fifth step this was disproved as
the number of ways was over 16.
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We Saw The Light......
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Theory 3
0
1
2
1
1
0
1
2
4
1 2 1
8
0
1
2
3
1 3 3 1
4
3
2
1
0
16
1 4 6 4 1
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Pascal's
Triangle
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Futher Investigation

• Once we had finally discovered a pattern for
  black and white strips we
• decided to further our investigation..
• WE FOUND SOMETHING AMAZING..
• New hypothesis The amount of colours used is
  the number you times
• by

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2 Colours No. of squares No. of combination
1 2
2 4
3 8 4
16
3 Colours No. of squares No. of combinations
1 3
2 9 3
27 4
81?
4 colours No. of squares No. of combinations
1 4 2
16 3
64?
5 colours No. of squares No. of
combinations 1
5 2 25
3 125?
6 colours No. of squares No. of combinations
1 6
2 36 3
212?
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Conclusion

• What was the point of this assignment?

While we had learnt that anything goes, this
investigation proved that ANYTHING really does go.

• Process is just as important as getting the answer

Fact Using excel we discovered that there are
33 554 432 different combinations using 25
squares and 2 colours.