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Guest Message by DevFuse
 

Prime

Member Since --
Offline Last Active Dec 03 2013 05:53 PM
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#336860 perfect powers

Posted by Prime on 02 December 2013 - 05:48 AM

Barring complex numbers and limiting ourselves to integers...

Spoiler for another possibility


  • -1


#329751 Knight Checker

Posted by Prime on 17 March 2013 - 04:54 AM

White seems to win in whichever way, provided it has the first move from that position.

Spoiler for example

 


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#329084 Stopping and Turning back hands of time

Posted by Prime on 25 February 2013 - 08:46 PM

Spoiler for

 

I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.

Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.

 

Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?

I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

 

Spoiler for actually, the answer is


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#329040 Congruent polygons

Posted by Prime on 24 February 2013 - 09:07 PM

Spoiler for Generalizable formula


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#327661 All numbers showing

Posted by Prime on 26 January 2013 - 05:23 AM

Spoiler for had thought...

 

 

Yes. Simple concept that cuts thru all the computational complexity.

This concept, does not apply to the question in the OP. The problem called for finding the minimum number of rolls (or dice) to get a winning bet. A winning bet is one, where your probability of winning is better than 0.5. It is not the same concept as average number of rolls (dice) required to get to the objective.

A simple example:

If you roll repeatedly a fair dice, then any given number, say "1", will occur on average once in six rolls. However, if I bet on "1" coming up just after 4 rolls or sooner, I am going to come out ahead. (Same as rolling 4 dice and betting that at least one of them will roll "1".)

P = 1 - (5/6)4 = 0.5177

 

The answer to the problem as stated is like Sp and myself have found. I have another equation, which is not recursive, but encompasses all variations. It yields the same result. I'll make a separate post for it.

 

But of course you still get a winning bet with 14.7 rolls. Your winning chance is better than 60%, but it is not the minimum number of rolls.


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#327606 All numbers showing

Posted by Prime on 24 January 2013 - 12:19 PM

I can get an answer, but no simple explanation. But that should do for everyday gambling needs.

Spoiler for The smallest m is...


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#327530 Ultimate Mate

Posted by Prime on 22 January 2013 - 09:35 AM

Found the ultimate mate in 9 moves.

Spoiler for the 9-move position


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#327396 Insert Coin Here

Posted by Prime on 17 January 2013 - 08:20 PM

Spoiler for

I wouldn’t classify winning with regular coins as “problem”. Just take the winnings home and measure the remaining two coins at leisure using your own precision scale.

 

But if you insist on using the coin operated balance to the end...

Spoiler for the weighing sequence


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#327335 Chess puzzle

Posted by Prime on 16 January 2013 - 08:04 AM

This puzzle is from one of Martin Gardner's books:

 

chesspuzzle2.jpg

 

The position on the diagram occured when the White King was knocked off the board.

1. Restore the White King to the appropriate square.

2. Find the last two moves.


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#327261 Hitting 137

Posted by Prime on 14 January 2013 - 09:32 PM

It seems to stand the reason...

Spoiler for just a guess


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#327245 Get the gold coin...

Posted by Prime on 14 January 2013 - 07:42 AM

A finishing touch...

 

Spoiler for The general formula

 

Armed with this knowledge, you could make a bet, whereby first your opponent sets up any position and then you choose who moves first.


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#326702 Foiled Again

Posted by Prime on 15 December 2012 - 06:54 PM

I have enjoyed this problem. It looks like something original in the old family of weighting problems. The solution I found seems to be the only solution.

Spoiler for Solution

I am curious as to how this problem was constructed.


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