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Math in its Prime…


A few years ago an old school textbook that H3 used explained that 1 was not a prime number “because of the Liquorice Factory”! The attached pdf is a great worksheet for students (and other readers of this blog) to examine the kind of machines that we need in order to produce liquorice in lengths from 1 –> 100. For example, if we put length “1” of liquorice into the #6 machine we will get out a length that = 6. But, wait a minute! Surely there is no need for a machine of length #1 since that is the length we start with? Therefore, the number 1 is NOT prime???

But, what happens when the #6 machine breaks down? Can we still produce a liquorice of length 6? Yes, but only if we use the #2 machine first, followed by the #3 machine! So, how many machines do we really need to produce all the liquorice lengths from 1 to 100?
prime factoryClick here for the full worksheet in pdf format:The liquorice factory

H3 confession: we did eat liquorice after posting this 🙂

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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