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Bearoff 8 cube

Posted By: Jason Lee
Date: Friday, 8 January 2010, at 1:52 a.m.

In Response To: Bearoff 8 cube (Matt Cohn-Geier)

MCG: Usually here I would estimate what 24.5 / 94 is but this looks like a pretty close decision and match-critical so I might as well calculate it exactly.

24.5 / 94 = 12.25 / 47 = 12.25 / 47 x 2.13 / 2.13 = 12.25 x 2.13 / ~100 = 24.5 + 12.25 x .13 = 26% or so.

What's the deal, you just happen to know that 100/47 ≈ 2.13?

Here's a division technique. To estimate B/(A+d) where d is small, use

B/(A+d) ≈ (B-e)/A, where e = Bd/A. Easiest to use when A is a "nice" number. The calculation is more accurate the smaller d is.

Here, B = 24.5, A = 100, d = -6. Then e = (24.5)(-6)/100 = (49)(-3)/100 = -1.47. Thus,

24.5/(100-6) ≈ (24.5 + 1.47)/100 = 25.97, compares well with the actual value (to two decimal places) of 26.06.

JLee

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