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(=2n-r, where nr is remainder). This
2n-r=4. Next exclusions are 4,
10, 16, [28 &c). But 16 from 20 = 4
& 2n-4=12-4=8. Next exclusions
are 8, 20 Now 20=2B, & that ends
it. Therefore total exclusions are
12, 4, 16, 8 or 4, 8, 12, 16.
This is correct.
Therefore the Rule of Rings may
be stated thus: Where z=1, an odd
no must not be addes to an even no,
nor an even no to an odd; where z
exceeds 1, if B is divisible by n, then
2n, 4n, 6n &c. up to 2B are excluded;
where B is indivisible by n, then (1)
2n, 4n, 6n &c up to 2B are excluded
remainder r difference, d,. (after of whichever
of these nos is next below 2B
from 2n, & this no. +2n, 4n &c. are
excluded & so on till a number is reached
which equals 2B.
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