bonanova

Since there are only three left, I've added a bonus: 14. WALIAYS

And welcome to the Den ..

I thought NO ONE would get that! Wait. No. <_< Kind of ingenious tho. Solved: 1 4 5 6 7 8 10 Still causing dandruff showers: 2 3 9 11 12 13

I'm working on both puzzles from scratch, and could use a clarification. No plurals means no nouns ending in S. [CAPES] Can we also assume no verbs are in 1st person singular [COPES] or are they fair game? - bn

Nice job. The connection is more apparent than might seem apparent, at first, or, something.

You're correct with all your answers. And 5 should read IDNHSRWTW! OP Amended

Yup. Typo.

What ties these to BrainDenizens? 7453 74275 73724 87688 725666 2277 9255393

One letter escapes me but

If IMO means In My Opinion, flesh these abbreviations out. ANWYCCDFY * prathibadev BCATSK * Sparanda CYCBI * SyWren GMLOGMD * PoudreAvenger IDNHSRWTW! * mafrofro IHAD * mafrofro JATB * mafrofro JBJBJATW * mafrofro KOTG * HokieKen KYEOTB * mafrofro MHMLW but TMCSTS * PT TPOPO <------------- remains a mystery TAFBEM * dedhed WALIAYS * HokieKen * = solved

You're on the right track, just need an "aha" moment ...

Yup. Nice job.

Agreed. [1] Integrals and sums are closely related; the smaller the intervals in the sum, the closer to an integral it gets. [2] Dice actually is a good teaching technique. You'd like students to be able to make comparisons to simpler tasks. Suppose I had the correct formula and worked through 7 pages of calculations, missed a factor of 2 somewhere and ended up with 2/3 as the result. If I thought the dice [or some other quick and dirty method] would give an approximate result and found .324, it could suggest that 1/3, not 2/3 is the correct answer and give me the encouragement I'd need to look for an extra factor of 2 in my calculations. That's what I meant by sanity check.... Nice puzzle.

Here's some code breaking and a bit of Googling, for good measure. Enjoy. 843 8432873 47 842 84464 4 5683 36464 6678. 4 4283 66 26688765 6837 2 3456. 4 366'8 5669 9428 9455 23 5338 66 843 2888464-7666 36567.

Topic has been posted before at least twice. Closed.

Nice puzzle Professor. Thanks.

I think your issue is well taken, within the confines of the OP. It would require very precise measurement to tell the difference in fall time due to weight difference. The methods I said would work were those for which even a possibly imperceptible difference occurs. Drop the coins in an elevator shaft filled with water, tho, and the difference is more easily seen. I said a method worked when there was a direct effect of density on the proposed observation. I also postulated a measurement apparatus that had sufficient precision to detect it. I said a method would not work when there was no direct effect by density on the proposed observation. For example, making a pendulum and observing the period. Only the length of the string matters there. In your cycling experience, I'm sure the drag at 70 mph is noticeable. And for your safety I hope you wear a helmet. For competitive purposes cycling helmets [and body positions] are studied carefully for air resistance. Electronic timers are sufficiently precise to measure the effect on arrival time when those matters are ignored, even for lesser speeds. But the OP did not place such sensitive instruments at our disposal.

Perhaps not, but perimeter points were not considered because you requested it. Check out post #6 on that matter. I wonder why you draw a distinction between circumference and circle and seem critical of those who don't. A circle divides the plane into interior and exterior regions; but a circle is defined as its circumference. A circle is the locus of points equidistant from its center. Specifically, a circle is not the locus of points whose distance from a central point is less than or equal to a certain value [radius]. That's the definition of a disk. As to the probability of random perimeter points, two procedures for generating random points were clearly described 1. At random on the circle. r=1; theta=random. Such probability is not zero - it's unity. 2. At random interior to the circle. Taking random points within a double unit square and rejecting them if distance from origin > 1. In this case it's possible, with a probability of zero, for points to land on the perimeter. I find that BrainDen'ers generally do not mind discussions of their posts when comments are offered in a positive and collegial manner. Let's try to encourage that by example. That's what makes this forum as popular as it is.