since there are so many writing and literature threads, I'm making a math thread.

I'll only post questions I made, including the ones I put on that vanguard forum who's url i lost.

1) sin(9!) degree mode


2) The letters in the word SEQUENCE can be arranged in a number of different ways; for example you can make QUENESCE or ECENUQES. If you arrange all the posibilities in alphabetical order so that CEEENQSU is first, and USQNEEEC is last, what is the 6700th arrangement?

3) Tim has ten large boxes. Inside some of these boxes, they contain 10 medium boxes. Inside some of the medium boxes, they contain 10 small boxes. There are 118 boxes that do not have any boxes inside them. How many boxes are there in total?

4) Ursula wants to buy some beef shank for her mother. There are two stores that are nearby, the freeport market, and the stonehenge store. One pound of beef shank costs 10 dollars at the freeport market. One pound of beef shank at the stonehenge store costs 50 dollars a pound. However, for every other pound you buy, you get 9% off the original price (until the 11th pound), so for example, if you buy two pounds, the first costs 50 while the second costs 45 dollars, if you buy three pounds, the first bosts 50, second costs 45.5, and third costs 41, but if you buy 12 pounds, the last pound is still 5 dollars. How many full pounds of beef shank does Ursula have to buy if she wants to get a better deal at the stonehenge store?

5) If a,b,c,d,e and f are all positive integers, find the maximum possible value of ade given that a+b+c+d+e+f=2009, and a>b>c>d>e>f.

6) What is the probability of getting 49 or less heads in 99 tosses of a fair 2-sided coin?