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#1 Puzzles and Games » Circles » 2009-09-05 19:55:25

uzurpatorul
Replies: 20

The following is a variant of a problem that appeared on a college entrance examination. In the figure below, the radius of circle A is 2 units, the radius of circle B is 3 units. Starting from the position shown in the figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle A first reach its starting point?
circles2.gif


Reference:
http://www.projecteureka.org/problem/question/561

#2 Puzzles and Games » The value of n » 2009-08-13 17:28:58

uzurpatorul
Replies: 5

Let n be a positive integer. If the equation x+y+z = n has 66 solutions
in non-negative integers x, y and z, then what is the value of n ?

#3 Puzzles and Games » Diaphatus » 2009-07-19 15:21:17

uzurpatorul
Replies: 4

Diophantus, the Greek mathematician known as the "Father of Algebra", supposedly had the following inscribed on his tombstone:
"Diophantus passed 1/6th of his life in childhood, 1/12th in youth, and 1/7th more as a bachelor.
Five years after his marriage, there was born a son who died four years before his father, at half his father's age."

How old was Diophantus when he died?

#4 Re: Puzzles and Games » Flys » 2009-07-11 07:28:20

Just in the sense that you have only one cut to get the half.(either half circle/or half meatball).

#5 Re: Puzzles and Games » Flys » 2009-07-11 05:12:31

She is allergic only to fly droppings, and she started having the allergic reaction. ;-)

#6 Puzzles and Games » Flys » 2009-07-10 19:21:21

uzurpatorul
Replies: 12

2 Problems:

1st:
You are visiting your girlfriend and she orders pizza. Your evil girlfriend has perfect eyesight and notices fly droppings in three places on the pizza. She is seeking revenge on you for refusing to babysit her poodle and proceeds to cut the pizza. Assuming that the droppings occurred independently and in random places, what is the probability (the solution format is x/y where gcd(x,y) = 1) that she will be able to cut a half-circle pizza slice with all three droppings in one half?

2nd:
A meatball has four fly droppings on it. These droppings, are in random places and you must calculate the probability (x/y format, gcd(x,y)=1) that you are able to cut a semi-sphere with all four droppings on one side.

#7 Puzzles and Games » confusable IDs » 2009-07-07 19:15:32

uzurpatorul
Replies: 4

The University is considering issuing new student ID cards (again!). Each student will be assigned a 5 digit identification number from 00000 to 99999. For ease in record keeping, the registrar has requested that any two ID numbers differ in at least two places. How many ID's could the registrar issue?

#8 Re: Puzzles and Games » Crossing the dessert » 2009-06-27 06:21:38

if you look at my explanation is pretty much your formula for n between 3 and 4

500(1 + 1/3 + 1/5 + k/7) = 800, where k = n - 3

Another cool thing i noticed looking at your formula is that you just proof that the series is divergent, and with the common constrains any desert can be crossed (of course n grows exponentially).


P.S.

here are 2 variations of the same problem:
http://www.projecteureka.org/problem/question/105
http://www.projecteureka.org/problem/question/298

#9 Re: Puzzles and Games » Crossing the dessert » 2009-06-26 19:41:43

Lets assume that your solution is the right one, and indeed with 3.44 loads we can cross 800 miles:

with 1 load , we can go 500 miles
with 2 loads , we can go 500(1+1/3) = 666.66
with 3 loads, 500(1+1/3+1/5) = 766.66

now, it means that 3.44 - 3 = 0.44 loads we can get (800 - 766.66)x7 (we need 7 trips now to make a cache of 3 loads)

0.44 x 500miles/load = 220miles , (800 - 766.66)x7 = 233.38

0.4666 x 500miles/load = 233.3 (much closer to the answer)

#10 Re: Puzzles and Games » Crossing the dessert » 2009-06-26 05:31:37

You general solution is right, however final answer is little over

.


P.S.

I guess I was craving for sweets when I spelled the title.

#11 Puzzles and Games » Crossing the dessert » 2009-06-25 19:33:40

uzurpatorul
Replies: 8

An  unlimited  supply  of  gasoline  is  available  at  one  edge  of  a  desert  800  miles  wide,  but  there  is  no  source  in  the  desert  itself.  A  truck  can  carry  enough  gasoline  to  go  500  miles  (this  is  called  the  "load"),  and  it  can  build  its  own  refueling  stations  at  any  spot  along  the  way.

What  is  the  minimum  amount  of  gasoline (in loads)  the  truck  will  require  in  order  to  cross  the  desert?

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