Lol... yeah, I realized that right after posting. I went back and changed it a minute before you postedPlease Register or Log in to view the hidden image! My basic reasoning here is that the volume is constant, so I calculated it with a hole of radius 0. As the hole grows, the sphere does too. To be any simple kind of answer, it has to be constant.
Right but WRONG Well, I screwed it up but it is really strange. I calculated Persol's first wrong answer backwards and got the right radius but running the TI-55 forwards I was getting incorrect answers for volume.. Wierd. I was looking to see if indeed the volume stayed the same but my results were saying they didn't. When actually they do. Good problem though Janus58.
Chicken & Eggs Disregarding the obvious that a half chicken doesn't exist, etc: If a chicken and a half, lays and egg and a half, in a day and a half. How many chickens does it take to lay a dozen eggs a day?
9's Question on mathematics. As a magician (40 years ago) I did many tricks by using a unique feature of 9's. Why is it that digits any multiple of 9 will add to nine? i.e. - 9 x 71485 = 643,365 6 4 3 3 6 5+ --- 27 2 7+ ---- 9 or 9 x 9 = 81 8 1+ ---- 9 And fractals of 9 also equal fractals of 9. 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 = 3 3 x 5 = 15 = 6 3 x 6 = 18 = 9 3 x 7 = 21 = 3 3 x 8 = 24 = 6 3 x 9 = 27 = 9 etc, etc., This 3, 6, 9 sequence continues forwver.
Re: 9's Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
Oh Yea everneo, Cake in a hat, never ending ping pong balls from a card. In "Cake in the Hat", I borrow a hat (deep like coyboy,etc) from the audience. My wife held it upside down and I crack an egg an put in it, pour a couple pints of milk in it, a cup of flour, etc. Stir it with my wand, heat it with a candle and wahla. I would dump out cup cakes or doughnuts. The hat (unless I was nervous), suffers no damage.Please Register or Log in to view the hidden image! PS: You don't want to play jpoker with me either. I can shuffle a desk of card until you say OK, pass the cards around for them to be cut by observers and then deal six full houses and an Ace high spade Royal Flush. Guess who gets the flush?
Not Exactly ryans, Not exacatly, those suckers are sharper than me. I tried some stuff in Black Jack once and was up $120.00, They gave me strange looks and the next thing I new I was holding a cup on the sidewalk selling penciles.Please Register or Log in to view the hidden image! Not actually but they did empty my billfold.
Re: Right but WRONG How did try calculating the volumes without using integrals? I don't know of any simple geometric way to do it, which is why I thought it must be constant.... riddles don't using integralsPlease Register or Log in to view the hidden image!
Geometry persol, Vt = 4*Pi*r^3/3 Volume Hole = Pi * r^2 * l Volume of Zones of one base = 2 * Pi * h^2 * (r -h/3) h = r - l
Re: Geometry Ahhh. That works too... I tried simplifying symbolically and got something wrong in there.
Re: 9's This has to do with the fact that 9 is the highest digit value in decimal. The same thing happens for 7 in octal, and F in hexidecimal. First off, we'll show that any digit multiplied by 9 will result in a product who's digits add up to nine. start with A*9, with A being any single digit number. this is the same as A*(10-1) or A*10 - A since A stands for a single digit we'll write A*10 as A0 which gives us: A0 -A Subtracting the 'ones column we have 0-A , borrowing the 'tens' column we get 10-A for our 'ones' digit of the product. subtracting the 'tens' column, we have (A-1 - 0) since we borrowed. earlier. giving us the product digits of (A-1) and(10-A) adding them gives (A-1+10-A) , the A's cancel out leaving 10-1 = 9 two digit numbers work like this: AB*9 AB*(10-1) AB0 -AB if B>A this gives digits of (A),(B-1-A)&(10-B) added together: A+B-1-A+10-B : A's and B's cancel out, Leaving 10-1 =9 B<A gives digits of (A-1),(10+(B-1)-A) & (10-B) added together: A-1+10+B-1+10-B A's and B's still cancel out, leaving -1+10-1+10 or (9+9) We've already shown that adding the digits of the sum of 9+9 or 2*9 will equal nine. three digits: ABC * 9 ABC *(10-1) ABC0 -ABC ..... and so on Its easy to see that no matter how many digits we have: The Individual digits(A B C's etc) cancel out The one's column produces a 10 which results in a -1 somewhere down the line. Every 10 produced by borrowing creates a -1 , meaning after you cancel out the individual digits, you are always left with at least one (10-1) pair each which reduces to a 9. result: the sum of the digits of any product of 9 equals 9 (in decimal)
