May 22nd, 2022 at 8:05:51 PM
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Quote:DJTeddyBear

I hate to say it, particularly since I've waffled on this topic myself, but Alan might be right. It's all about the wording.

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Thank you. Yes, it's all about the wording.

1/11 is the correct answer to the "challenge question."

May 23rd, 2022 at 6:17:45 AM
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Quote:Dieterpi has been voted to be 3 and 22/7.

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I throw the challenge flag at that.

There is an urban legend that Alabama's legislature voted to redefine pi as 3, to be in agreement with the bible. However, it isn't true.

Source = Snopes.com

You might say another governmental body did make such a vote, to which I respectfully ask for evidence. Thank you.

It's not whether you win or lose; it's whether or not you had a good bet.

May 23rd, 2022 at 6:22:13 AM
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Quote:WizardQuote:Dieterpi has been voted to be 3 and 22/7.

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I throw the challenge flag at that.

There is an urban legend that Alabama's legislature voted to redefine pi as 3, to be in agreement with the bible. However, it isn't true.

Source = Snopes.com

You might say another governmental body did make such a vote, to which I respectfully ask for evidence. Thank you.

link to original post

Indiana Pi Bill, according to Wikipedia, which I know is not the best source.

The difference between fiction and reality is that fiction is supposed to make sense.

May 23rd, 2022 at 6:43:11 AM
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Quote:WizardQuote:Dieterpi has been voted to be 3 and 22/7.

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I throw the challenge flag at that.

There is an urban legend that Alabama's legislature voted to redefine pi as 3, to be in agreement with the bible. However, it isn't true.

Source = Snopes.com

You might say another governmental body did make such a vote, to which I respectfully ask for evidence. Thank you.

link to original post

Indeed, I had misremembered numerous anecdotes over the years.

Bill #246 of the 1897 Indiana General Assembly included a proposed method for squaring the circle.

Wiser heads seem to have prevailed.

https://journals.iupui.edu/index.php/ias/article/view/4753/4589

I am sorry for throwing a wrench in the works with bad memory.

I stand by the principle that popular vote cannot change how math works.

May the cards fall in your favor.

May 23rd, 2022 at 7:38:41 AM
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Quote:billryanAbsolutely, although Mike has first dibs. If Mike passes, I'll gladly play the house. I may no longer be bound by math, but I know a great opportunity when I see it.

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Thank you for offering me first dibs. It's a free market, so you two may have a challenge on your own. I'll just say that I'll offer 8 to 1 odds on two 2's to anybody, subject to mutual agreement on the bet amounts and payment terms. As far as I'm concerned CB, or anybody, may choose whom (or is it "who"?) to do business with.

It's not whether you win or lose; it's whether or not you had a good bet.

May 23rd, 2022 at 7:52:10 AM
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Once I came to realize how flexible math can be, I realized everyone was wrong about this.

Two dice are thrown, and one is a six. What are the chances the other die is a six. Some of you are claiming 1/11, others are claiming 1/6. I say you are all overthinking it.

The other die is a six or it isn't. 50-50.

The key is making sure you understand that math is not static.

If I write 2+2= 5, you'd say I was wrong. Most would say you need to add a one to the equation to get it right 2+2+1=5. I choose to add a letter. 2+2A=5. If I claimed 50 + 311 = 672,567 people would mock me, but write 50A+ 331X=672,567 and people accept you as one who knows.

The New Math was right all along. No wonder people hated it.

Go ahead and cling to your guns and your old math.

As the prophet wrote:

Don't criticize what you can't understand

Your sons and your daughters

are beyond your command.

Your old math is rapidly changing

Two dice are thrown, and one is a six. What are the chances the other die is a six. Some of you are claiming 1/11, others are claiming 1/6. I say you are all overthinking it.

The other die is a six or it isn't. 50-50.

The key is making sure you understand that math is not static.

If I write 2+2= 5, you'd say I was wrong. Most would say you need to add a one to the equation to get it right 2+2+1=5. I choose to add a letter. 2+2A=5. If I claimed 50 + 311 = 672,567 people would mock me, but write 50A+ 331X=672,567 and people accept you as one who knows.

The New Math was right all along. No wonder people hated it.

Go ahead and cling to your guns and your old math.

As the prophet wrote:

Don't criticize what you can't understand

Your sons and your daughters

are beyond your command.

Your old math is rapidly changing

The difference between fiction and reality is that fiction is supposed to make sense.

May 23rd, 2022 at 1:00:38 PM
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Here is a different way to illustrate the logic of the two dice problem.

I understand that AlanMendelson will not agree with anything that contradicts his own idea, so this is aimed at others in the forum. I am trying to innovate on how to explain the logic of the solution of the 2-Dice problem.

Given: Two dice have been rolled in a cup, Joe's assistant has been instructed to say "at least one of the dice is two" after looking at both dice in the cup if and only if that statement is indeed true. Joe's assistant does look at both dice and then he does indeed make that statement.

Now, we blindfold our contestant Joe. Joe's assistant reaches under the cup and without looking at either of the dice, grabs one of the dice, removes it from the cup and places it in Joe's outstretched hand. Joe makes a fist around the die in his hand, so it cannot be seen. His blindfold is then removed.

Now we ask: "Joe, what is the probability that the dice that is still in the cup is a 2?"

And Joe replies: "if the die in my hand is a 2, I know the other die has a 1 in 6 chance of being a two. And therefore the odds of both dice being 2s is 1/6. I have already posted that statement a zillion times during the past week."

And, the assembled Elder Council of WOV Math Geeks chime in and say : "We agree with every part of that statement."

"BUT" the Wizard asks "What if the die in your hand is not a 2? What, then is the chance that the other die in the cup is a 2?" Joe starts to answer, then stops and thinks carefully. He then responds "the chance of the other dice being a 2 is 100% -not 1/6 - because I have been told that at least one of the dice must be a 2 and so it must be the die in the cup. And, of course, I also conclude that there is ZERO probability that both dice are a 2, because in this scenario the die in my hand is not a 2 !!!!!"

The Elder Council of WOV Math Geeks gently point out "Remember that the die in your hand was randomly removed from the cup and you have no further information about it. You can't just assume that it is a 2 and that the other die has a 1/6 chance of being a 2, because you must also take into account that the die in your hand may NOT be a 2, and that therefore the other die (in the cup) has a 100% chance of being a 2."

"Because to assume that a die in your closed hand is a 2 is to assume knowledge that you were not given in the statement of the problem."

Joe says "But I want to start with the knowledge that one of the dice is a two and make this a one die problem, that is, it is a problem of whether the other six-faced die is a two."

And the Elder Council responds: 'But there is no way to actually start with a die that is a 2 without peeking at it to determine it is a 2. You must accept that any die you select has a 6/11 chance of being a 2 and a 5/11 chance of not being a 2. Therefore, the other die will, respectively have either a 1/6 chance of being a 2 or a 100% chance of being a 2."

There is a 6/11 chance that any die you pick will be a 2, and in that scenario there is a 1/6 chance that the other die will also be a 2.

Thus, 6/11 x 1/6 = 1/11.

(Note: edited the name of the imaginary participant.)

I understand that AlanMendelson will not agree with anything that contradicts his own idea, so this is aimed at others in the forum. I am trying to innovate on how to explain the logic of the solution of the 2-Dice problem.

Given: Two dice have been rolled in a cup, Joe's assistant has been instructed to say "at least one of the dice is two" after looking at both dice in the cup if and only if that statement is indeed true. Joe's assistant does look at both dice and then he does indeed make that statement.

Now, we blindfold our contestant Joe. Joe's assistant reaches under the cup and without looking at either of the dice, grabs one of the dice, removes it from the cup and places it in Joe's outstretched hand. Joe makes a fist around the die in his hand, so it cannot be seen. His blindfold is then removed.

Now we ask: "Joe, what is the probability that the dice that is still in the cup is a 2?"

And Joe replies: "if the die in my hand is a 2, I know the other die has a 1 in 6 chance of being a two. And therefore the odds of both dice being 2s is 1/6. I have already posted that statement a zillion times during the past week."

And, the assembled Elder Council of WOV Math Geeks chime in and say : "We agree with every part of that statement."

"BUT" the Wizard asks "What if the die in your hand is not a 2? What, then is the chance that the other die in the cup is a 2?" Joe starts to answer, then stops and thinks carefully. He then responds "the chance of the other dice being a 2 is 100% -not 1/6 - because I have been told that at least one of the dice must be a 2 and so it must be the die in the cup. And, of course, I also conclude that there is ZERO probability that both dice are a 2, because in this scenario the die in my hand is not a 2 !!!!!"

The Elder Council of WOV Math Geeks gently point out "Remember that the die in your hand was randomly removed from the cup and you have no further information about it. You can't just assume that it is a 2 and that the other die has a 1/6 chance of being a 2, because you must also take into account that the die in your hand may NOT be a 2, and that therefore the other die (in the cup) has a 100% chance of being a 2."

"Because to assume that a die in your closed hand is a 2 is to assume knowledge that you were not given in the statement of the problem."

Joe says "But I want to start with the knowledge that one of the dice is a two and make this a one die problem, that is, it is a problem of whether the other six-faced die is a two."

And the Elder Council responds: 'But there is no way to actually start with a die that is a 2 without peeking at it to determine it is a 2. You must accept that any die you select has a 6/11 chance of being a 2 and a 5/11 chance of not being a 2. Therefore, the other die will, respectively have either a 1/6 chance of being a 2 or a 100% chance of being a 2."

There is a 6/11 chance that any die you pick will be a 2, and in that scenario there is a 1/6 chance that the other die will also be a 2.

Thus, 6/11 x 1/6 = 1/11.

(Note: edited the name of the imaginary participant.)

Last edited by: gordonm888 on May 23, 2022

So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.

May 23rd, 2022 at 1:39:48 PM
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This thread reminds me of a Happy Days episode where Fonzie couldn't get the words "I was wrong" out of his mouth

May 23rd, 2022 at 2:21:35 PM
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Humanity beats conformity.

The difference between fiction and reality is that fiction is supposed to make sense.

May 24th, 2022 at 12:21:27 AM
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It's creative, but it's different situation than somebody rolling two dice, looking at them, announcing that the number "x" is showing on at least one of the dice and then asking what the probability that the other dice also shows "x".

I mean, the number "2" is a nice number and all but if you substitute in an "x" instead it makes all the confusion go away and you can then see that the odds of the other dice being "x" is 1 out of 6

I mean, the number "2" is a nice number and all but if you substitute in an "x" instead it makes all the confusion go away and you can then see that the odds of the other dice being "x" is 1 out of 6