Alison Kiddle says her dad bought himself a new mincer. She asks “How many holes? How would you count them?”
Problem of the Week
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Mincer Holes
Answer:
One way to count holes (or calculate areas) efficiently, is to look for symmetry.
In the case of this mincer, it has both rotational and line symmetry.
The red lines in the photo below show that it has rotational symmetry order 6.
The additional dotted green lines in the next photo, show that within each of the sectors marked by the red lines, there is a line of symmetry marked by the dotted green line.
This makes 6 x 2 = 12 sectors altogether, each sector having the same number of holes.
The number of small holes is in each sector is 3 + 4 x ½ = 3 + 2 = 5 small holes.
There are 12 sectors, so 12 x 5 = 60 small holes.
We then have to add one more for the large hole in the middle, so the total number of holes in the mincer is 61 holes.