bonanova

That rings the bell. Well earned. Another form is nC4 + n-1C2 + n

Close, but the number that follows 16 is 31.

but 1.01 for r1 is stepping on the line..the limit is 1 The incircle has radius of 1. Good catch ... The competition is still open. I'll mark it solved at 74.13 until/unless a better number comes in.

Are some boxes empty?

I love this puzzle.

Clue?

What are the rules? Arithmetic, or pattern?

I programmed the Malfatti circles for this problem. They give 66.27% coverage, thought initially to be optimal, clearly not.

OK I have it.

Sounds almost intuitive when put that way, and no arcane expressions. Nice solve. Never mind counting the days, a percentage is fine. I hope the residual methane fumes clear up soon!

Correct. The star awaits the formula.

Hi cantidad and welcome to the den. Close but that is not the answer.

You want to divide a pizza into a number of slices, but you're tired of going through the center all the time. So you adopt the strategy of marking points on the circumference of the pie and making slices along all the chords that they pairwise create. At last week's pizza party you attempted to make 32 pizza chunks, from a very large pie, by this method. How many points did you have to mark off on the pizza's circumference to give you and your 15 guests at least 2 chunks each? Bonus: The coveted bonanova gold star will be awarded if you give the formula for calculating pieces from points. This gives you an idea:

The findings of the Huygens probe indicate that Titan (Saturn's largest moon) has a nitrogenous atmosphere that periodically produces rain onto that moon's surface. Titan and Earth are the only known heavenly bodies with liquid rain. But given its hostile temperature of -180oC Titan's rain is not water, it's liquid methane. But enough of the cold facts. The exciting part of this puzzle is that in 2004 you were given a large supply of beef jerky, a warm parka, and the job of being Titan's chief in-person, feet on the ground, up close and personal, weather observer. Upon your recent return, you reported your findings on Titan's rain activity. Let's call the days on Titan that it did not rain "sunny" days, even with the constant nitrogenous smog. (You grew up in Los Angeles.) You found that sunny days on Titan were followed by another sunny Titan day 29 days out of 30, (pss = 29/30), while rainy days were followed by another rainy day with probability prr = 0.7. Like many heavenly satellites, Titan's rotation is tidally locked to its orbital period (16 Earth days.) If you were on Titan for say 9 Earth years, on about how many Titan days did you observe rain?

yes, your example is 2 steps. It's not my example. Check 37-14.