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:D :D 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?
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.
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:confused:Code:
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
i'd think phan wants smallest # of apples. of course, remember that half of half must still be an integer.
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 ;) ;) ;)
nobody can?if not,i'll show my solution,ok? :D :D
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.
thats not a good way,its so long,complicated...do u wanna see mine? :D
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!
its not very good,another way? :D :D
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.
Ok phan, so what is your way, which is so much better than all of ours?
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.
sorry ,i cant access to vbforum for 2 days cuz i'm lack of money :D :D :)
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 seventh:(x+1)2^7
so the general equation is :
(x+1)(1/2+1/2^2+......+1/2^7)=x
=>x=127
:D ;) :D
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!