10276 - Hanoi Tower Troubles Again!

[yatsen]

I can find the fomula between f(x) and f(x-1) by observation.
And it really work!
But I can't prove it in math.
Can anyone prove the formula ?

[shamim]

I can find the fomula between f(x) and f(x-1) by observation.
And it really work!
But I can't prove it in math.
Can anyone prove the formula ?

I was wondering, what is the formula.

I got Ac using simulation.

[yatsen]

f = f[i-1] + ((i-1)/2+1)*2

[CDiMa]

f = f[i-1] + ((i-1)/2+1)*2

You can rewrite this as f=f[i-1]+i+1 but I don't think it really works...

Ciao!!!

Claudio

[Sedefcho]

You can not rewrite the formula in that way, Claudio.
That's because the division Yatsen gives in his formula
is an integer division ( 50/2 = 25, 51/2 = 25 ).

This means that if K = (i-1)/2
then 2*K is not always equal to (i-1).

Yatsen, it is interesting to know how you derived that
formula. I guess by some inductive way of thinking.
Then most probably if you want a clear mathematical
proof you should just follow your inductive way of
thinking which has helped you to derive the formula.

Seems an interesting math task though to prove
your formula ( if it is always correct of course ).
There's still some minor chance that it works for i = 1,2,...,50
but it does not always work.

[CDiMa]

You can not rewrite the formula in that way, Claudio.
That's because the division Yatsen gives in his formula
is an integer division.

You're right, too careless of me...

Ciao!!!

Claudio

[hamedv]

what's wrong with my code???

Code: Select all

ACed

[hamedv]

Finally i got ac;
for n = 2 my optput was wrong

[poixp]

I have a little misunderstood. We need to put ball with number x and there are couple of pegs where it possible, should we simulate all possible placing or can we prove that any will do?
First I use simulation of all possibilities but it takes too long, than I tried to place ball on first possible place and get Ac. But, why I can do so?

[Shafaet_du]

input:

Code: Select all

5
1
2
3
40
30

output:

Code: Select all

1
3
7
839
479

happy programming