A Interesting Problem

[phanbachloc]

THE PROBLEM IS AS FOLLOW:
I have a number of apples, i give half of them and half of apple to Bush ,then i give half of the rest and half of apple to britney,..and i keep on giving half of the rest and half of the apple to someone until the seventh

i ask u how many apples do i have?

[snakeeyes1000]

we cannot answer that because you don't tell us how many apples you end up with. I assume it is 0, nas also your question means "how many did I start with". The problem is simplified by an equation of my invention, .5x-.5=y, where y is the next about of money you have and x is the current amount of money.

8.     0:     --     --
7.     1:     .5     .5
6.     3:     1.5    .5
5.     7:     3.5    .5
4.     15:    7.5    .5
3.     31:    15.5   .5
2.     63:    31.5   .5
1.     127:   63.5   .5

my answer, as I understood the question, is 127 apples to begin with,. If this was the wrong concept, forgive my English and correct me so that I may feel like an ass

[bugzpodder]

i'd think phan wants smallest # of apples. of course, remember that half of half must still be an integer.

[phanbachloc]

yeah,i have 127,but that 's not the solution
u just find out blindly.please use math!!!! anyway,thats very good,u're very good

[phanbachloc]

nobody can?if not,i'll show my solution,ok?

[Kalkewl8ter]

Let n be the original number of apples.
1/2(1/2(1/2(1/2(1/2(1/2((1/2)*n-1/2)-1/2)-1/2)-1/2)-1/2)-1/2)-1/2
=1/2(1/2(1/2(1/2(1/2((1/4)*n-3/4)-1/2)-1/2)-1/2)-1/2)-1/2)
=1/2(1/2(1/2(1/2((1/8)*n-7/8)-1/2)-1/2)-1/2)-1/2)
=1/2(1/2(1/2((1/16)*n-15/16)-1/2)-1/2)-1/2
=1/2(1/2((1/32)*n-31/32)-1/2)-1/2
=1/2((1/64)*n-63/64)-1/2
=(1/128)*n-127/128
The smallest positive integer for n in order for the above expression to be a non-negative integer is 127. Thus, you originally had 127 apples.

[phanbachloc]

thats not a good way,its so long,complicated...do u wanna see mine?

[bugzpodder]

shouldn't be that bad!

for the smallest case i have 0 apples left:

so i must've gotten 1 apple before i gave it to you, phan .

(0+1/2)*2

means i must've gotten 3 apples for Taotao.

same, (1+1/2)*2, not gonna show it again

means i must've gotten 7 apples for Mr. White.

means i must've gotten 15 apples for John Sun.

means i must've gotten 31 apples for Laura.

means i must've gotten 63 apples for Brittany.

means i must've gotten 127 apples for Bush.

lets look at the expression:

basically you take the kth term, add 1/2 and multiply by 2 to get k+1th term (depending on how u look at it k-1th term). note this is a special case of an arithmatic-geometric progression
so a general formula would be:

(2^k)(n+1)-1. as kalkewlat8r indicated n cannot be -ve so we make it 0.

so easy eh? i can figure out the answer no matter how many ppl i gave apples to. if u tell me that you have c apples left i can still figure out really really fast using my formula

^-^__Cheers!__^-^ Massey RuleZ!

[phanbachloc]

its not very good,another way?

[bugzpodder]

i am satisfied with my way! (actually this is for testing out my new signature lol)

btw phan what makes it a good way, Phan? maybe only your way? Prove me wrong by showing your way and tell me why it is good.

[Kalkewl8ter]

Ok phan, so what is your way, which is so much better than all of ours?

[snakeeyes1000]

you are either a mathematical genius or a tad slow... We all three had good answers. Took me 5 seconds to actually figure out the way to solve it, and 20 seconds to graph all the information. I am sure kate's and bugz's solutions are even faster than mine, so you're must be great.

[phanbachloc]

sorry ,i cant access to vbforum for 2 days cuz i'm lack of money
the number of apples i gave to bush is:
x/2+1/2=(x+1)/2
the second:
1/2(x-(x+1)/2)+1/2=(x+1)/2^2
.....the seventhx+1)2^7
so the general equation is :
(x+1)(1/2+1/2^2+......+1/2^7)=x
=>x=127

[bugzpodder]

lets see ur formula when what if there is 5 apples left after given to 7 ppl?

mine lets me find it really fast:

(2^k)(n+1)-1

(2^7)*6-1=128*6-1=767

and u haven't told me why ur formulae is better!