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BMAD added an answer to a question Cutting a circle to find a point part two
Interestingly I believe i found the theoretical probability to be 50% but my simulations have it around 6062%.

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BMAD added a question in New Logic/Math Puzzles
Dash?There is an old game that I learned back in my home country when I was a child but the name escapes me. When teaching it to my students, I call it 'dash' whose meaning will be obvious.
Setup the 'game board' as follows: Row 1: 1 dash, Row 2: 3 dashes, Row 3: 5 dashes, and Row 4: 7 dashes

  
    
      
The requirements of the game are simple:
Each player takes turns circling any amount they like in any row. Each player must circle at least 1 notcircled dash on their turn. A player does can circle dashes that are not adjacent. The player may not circle dashes in more than one row in a single turn. The last player to circle a dash is the loser.Is the advantage for the first player or second player or is this a fair game?
 1 reply
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BMAD added a question in New Logic/Math Puzzles
Cutting a circle to find a point part twoThis is an extension of my previous question. I honestly am torn between two different solutions (one found in theory and the other in simulation). I am curious what solution we will find here.
Recall that we have a unit circle where three random points define three arcs. What is the probability that the longest arc contains the point (1,0)?
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BMAD added a question in New Logic/Math Puzzles
The distribution of piAre the digits that represent pi (e.g. 3.1415926....) a uniform distribution?
What if we examine pi in base 2, is it a uniform distribution?
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BMAD added an answer to a question Limited Predictive Ability
would this not imply that the first two rounds use for the magic power are worst. Imagine that you are trying to beat your best score, your opponent is yourself. An opponent with the exact same power. Trying to do the best in this case, according to your previous post would include using this power at the end. Hence there is an advantage.

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BMAD added an answer to a question Limited Predictive Ability
my suspicion is that given that most people would pick a particular round to use their ability that there is in fact a particular advantage even if the expected payouts are the same. Maybe game theory should be utilized here over strict statistics??

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BMAD added an answer to a question cutting a circle to find a point
Where is my flaw...
*contains what i believe to be the solution*

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BMAD added an answer to a question Limited Predictive Ability
i wanted 4 rounds so my apologies. There should be 16 teams. Each game has a 5050 chance of being picked by you in that you have no knowledge of who you should pick though one team may or may not be better than the other team.

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BMAD added an answer to a question cutting a circle to find a point
Hmmm i am not sold that the answer Isnt

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BMAD added a question in New Logic/Math Puzzles
April Fool's Day and the typewriterOn April 1st a typist found the hammers of the typewriter resoldered in an arbitrary order, so typing a text resulted in gibberish. The typist decided to type a document in its entirety using this typewriter. Afterwards, if the result does not represent the original text, he will type the result, and so on. Prove that the clear text will emerge sooner or later. How many iterations are enough to guarantee that the clear text will appear, if the typewriter has, say, 46 keys? N keys
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BMAD added a question in New Logic/Math Puzzles
cutting a circle to find a pointChoose, at random, three points on the circle x2+y2= 1. Interpret them as cuts that divide the circle into three arcs. Compute the expected length of the arc that contains the point (1, 0).
 11 replies
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BMAD added a question in New Logic/Math Puzzles
Limited Predictive AbilitySay you are granted the ability to know the outcome of two consecutive rounds in a 8team elimination tournament. Each round that you win, the amount you bet is doubled while losing any bets when you pick the wrong team. Every round you take all of the money in your possession and split it evenly over each team that you believe will win. Is it in your best interest to use your ability of foresight in the first two rounds, middle two rounds, last two rounds or does it not matter?
 11 replies
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BMAD added an answer to a question Roll Them Out
Oh, i think the issue is the assumption (or a poor translation) behind what i meant when i said it is long enough to hold 11 balls. Clearly a chute that can hold 12 can also hold 11. The task was to find the smallest such chute that can hold 11 balls and allow the black balls to exit.

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BMAD added an answer to a question Roll Them Out
hmm, I see where I remarked that a chute shorter than 15 were possible but I am unsure of a solution of a size less than 12.

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BMAD added an answer to a question A loaded coin
both excellent answers.

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