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Bonus: Decatholitic formula & Download
Solve the formula in the download below, using existing answers. Value of correct answer: 500 points. Answer is rational. 10
Download The Puzzle Decathalon Word document!
Comments
If, in the Decatholitic Formula, one of the variables (6A eg.) is "Kangaroo 28", are we to express that value as simply "28"?
Posted by: DonV | Feb 6, 2005 1:27:45 PM
Unless I have made a mistake, there are no answers in the formula that would have nomenclature like "Kangaroo 28", unless it was something tricky like "natural log number 14" which would be, in geeky math terms, ln(14), which has a numerical value. I have so indicated in the rules that there are a few oddball answers like that.
Posted by: Michael | Feb 6, 2005 4:27:18 PM
Okay - I'm officially experiencing the "let-down". Would the doctor call it "Post-Puzzle depression"?
Posted by: Paula | Mar 1, 2005 1:17:33 PM
The Formula was very tricky, although it was solved correctly by one contestant. The major part of the formula reduces down to (root 2 x ((root 3) - 1))/sin 15, which has the unusual proprety of reducing down to 4 (fiddly math, but even MS excel will bring it to 4 if you have the right numbers). With other amounts plugged in, the grand total is 10.
Posted by: Michael | Mar 1, 2005 6:43:58 PM
Michael, I know I'm probably stating the obvious, especially for the one contestant who solved the formula correctly, but sin 15 could be substituted directly without having to use Excel by recognizing the angle measure as the difference of 2 special angles for which there are already simplest forms for sine and cosine measures.
Using the identity sin (A-B) = (sin A)(cos B) - (cos A)(sin B),
sin 15 = sin (45-30)= (sin 45)(cos 30) - (cos 45)(sin 30) = (sqrt(2)/2)(sqrt(3)/2) - (sqrt(2)/2)(1/2) = [(sqrt(2)/4)(sqrt(3)-1)].
So, with sin 15 in the denominator, the reciprocal of that ratio allows the square roots to cancel with the "major" part of the formula, leaving just the value of 4 to be used with the rest of the formula.
Nice one!
Posted by: Sean F | Mar 2, 2005 3:05:16 AM
Right on, Sean. I didn't want to get into that - but that's the math alright. I had the Galatians V clue, and I thought - now how am I going to get this to cancel out without finding a weird cosine answer? I used that exact formula, and then created questions (and the formula) so it would all cancel.
Posted by: Michael | Mar 2, 2005 6:51:29 AM
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