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#1 Re: Help Me ! » 64 pawns » 2015-06-27 17:33:12

I do not think I will be able to produce a very mathematical solution, sorry.

I liked this problem. Post more of these!

#2 Re: Help Me ! » f(f(n)) » 2015-06-27 17:30:18

Okay. Do you know why you revived this thread?

#3 Re: Help Me ! » 64 pawns » 2015-06-27 05:16:17

Why do you want a more "mathematical" solution?

#4 Re: Help Me ! » 64 pawns » 2015-06-26 12:33:03

See the Brilliant link and click on Reveal Solutions

#6 Re: Help Me ! » 64 pawns » 2015-06-26 02:47:20

Yes, but if you think it is very far away from mathematics, you're wrong.

Many interesting Combinatorial problems requires computational power for solving. But does that mean computers can reduce the problems into pure bashing? Nope! As you can see there, the backtracking solution can only solve upto the 10 by 10 chessboard whereas the one supplemented by enough research can solve upto a 174 by 174 chessboard.

I found another solution (much like this one) on another forum: https://brilliant.org/problems/too-many … hessboard/

#7 Re: Help Me ! » A problem with remainders modulo 2012 » 2015-06-26 01:04:29

If a < b (mod 2012) shouldn't ka < kb (mod 2012)?

#8 Re: Help Me ! » 64 pawns » 2015-06-26 00:44:04

You will need a computer for this: http://codegolf.stackexchange.com/quest … hess-board

One solution is a backtrack solution. Another guy (elsewhere) gave me a gf solution which I did not really understand that well.

#9 Re: Help Me ! » 64 pawns » 2015-06-25 04:25:51

I have reasons to believe the answer is 6148.

@phanthanhtom, Could you please look into this?

#10 Re: Help Me ! » simple logic yet difficult » 2015-06-25 01:28:11

No, you have got long grasses in your backyard. Also. You have got bottles of soy sauce

#11 Re: Help Me ! » simple logic yet difficult » 2015-06-24 22:04:53

Just use the large text box.

If you had a phone you would not need to buy a car, you could've just called the people you want to visit

#12 Re: Help Me ! » simple logic yet difficult » 2015-06-24 21:29:08

That is really a good thing about Alice.

Here is my kaboobly doo machine: http://kabooblydoo.appspot.com

It works on the principle of Predictive text

#13 Re: Help Me ! » simple logic yet difficult » 2015-06-24 20:55:49

Is Alice a member here?

Predictive texting is fun. Have you seen my Kaboobly Doo machine?

#14 Re: Help Me ! » Write a positive integer as the sum of powers of 2 » 2015-06-24 20:43:08

Nope. He proved the other thing too.

When f(n) is not of that form, the odds pair up

#15 Re: Help Me ! » Write a positive integer as the sum of powers of 2 » 2015-06-24 03:23:50

We are using strong induction here.

First we show that it is true for some of the beginning values by computation.

Then, we assume that for some value n, all of the preceeding values show the proposed property.

We now need to show that n also shows the same property, to complete the induction.

Note that f(n) = f(n-2^0) + f(n-2^1) + ... + f(n-2^k) + ...

We're interested in if any of these are odd. By the induction hypothesis, if there is such a term, it should be of the form 2^j - 1. This is because we've chosen to accept that only the output of such numbers are odd.

So, n - 2^k = 2^j - 1

#16 Re: Help Me ! » 64 pawns » 2015-06-23 12:50:18

This is a combinatorial search problem.

I think we should start writing a backtrack solver. I do not know how much time this method would take but at least we will discover a good many of the configurations

#17 Re: Help Me ! » simple logic yet difficult » 2015-06-23 12:08:59

math9maniac wrote:

Hi Agnishom;
     Tell me something. What relationship exists between Bob and Alice?

https://en.m.wikipedia.org/wiki/Alice_and_Bob
protocol.png

#18 Re: Help Me ! » simple logic yet difficult » 2015-06-23 06:14:43

Bob can send encrypted messages to Alice. He does not find cellular networks secure.

#21 Re: Help Me ! » Write a positive integer as the sum of powers of 2 » 2015-06-23 04:03:39

You did not have the proof. You did not even attempt it.

#23 Re: Dark Discussions at Cafe Infinity » Fiber Optics? » 2015-06-22 07:10:10

No matter how fast light is, the bottleneck effect counts.

#25 Re: Help Me ! » Write a positive integer as the sum of powers of 2 » 2015-06-22 06:28:15

Over OEIS? Why should they care if some values are even?

Calvin gave me a proof

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