# howardl1963

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1. howardl1963 added a post in a topic

I'm definitely in over my head from a math theory perspective, I just found the answer to be interesting from a logic perspective. Clearly, the answer approaches 50%, but I also think it approaches from the high side, which is all the puzzles was looking for.You definitely wouldn't be looking to make any large bets at even money.

I was talking to another friend about this puzzle and he preferred to think about a uniform function that produces numbers from 0,1, where each number is as likely as any other. So two questions.

1. Let's say that you know the function and after I use the function to produce two numbers, you use the function to produce one number. You then look at the first of my two numbers and switch if it's smaller than your number and stay if it's bigger. What are your odds of ending up with the bigger of my two numbers?

2. Since you know that the function produces a smooth distribution from 0,1, you use the optimal strategy, which is to stay with the first number is it's larger than .5 and switch if it's smaller. If you use that strategy, what are your odds of ending up with the larger number?
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2. howardl1963 added a post in a topic

I would imagine it's possible. Though I would assume, given a reasonable function, that the chances of that happening is very close to 0% and wouldn't affect your odds very much.
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4. howardl1963 added a post in a topic

Clearly, whatever the answer is, it will hit on philosophical questions and theoretical math. I talked long and hard and asked many questions of my math PHd friend. He is completely aware of the fact that there are infinite real numbers between any two real numbers, or above and below a single real number. He is still convinced you can do better than 50-50.
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5. howardl1963 added a topic in New Logic/Math Puzzles

I will choose two real numbers using a function that will produce numbers from -infinity to +infinity. You have no idea what function I'm using. It doesn't have to normally distributed.

I will write those two numbers on two different pieces of paper. You will look at one of the numbers. You can then choose whether to stay with that number or switch. You goal is to come up with a method to end up with the higher number more often than 50%. As long as your method is 50.000000.....000001% (probably the best you can do), you have solved it. Enjoy!
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6. howardl1963 added a post in a topic

This thread took a few days to get going but eventually didn't disappoint. Nicely done plainglazed. About a week ago, I thought of this triple balance scale concept and how quickly you can glean a massive amount of info after a few weighings. 16 seemed like such a simple and efficient answer, but i'm not surprised that this forum blew that away. Glad I didn't spend a long time writing out my solution for 16 now. LOL

These kinds of problems are always tougher to write out than to think about.
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7. howardl1963 added a post in a topic

I agree with this number. I'll let bishindo post his solution first. I'll post mine later if we don't hear form him today.
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8. howardl1963 added a post in a topic

You would be able to do 6 marbles in 2 weighings easily like this. However, if you read my first reply, you are allowed 3 weighings, which will allow for many more:

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9. howardl1963 added a post in a topic

Yea. That's what makes this one tricky.
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10. howardl1963 added a post in a topic

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11. howardl1963 added a topic in New Logic/Math Puzzles

There is a new kind of balance scale that has three weighing pans. When you put things in the pans, the pans will indicate the relative heaviness of each thing or group of things being weighed. For example, if something in pan one weighed 3, and the thing in pan two weighed 4 and the thing in pan three weighed 5, pan three would hang lower than pan two which would hang lower than pan one. Likewise, if you weighed things that were 4, 4 and 2, the pan with the 2 in it would hang higher than the other two pans, which would hang at the same height.

There are a group of marbles that all look exactly alike. Genuine marbles weigh 10. But, you know there is a counterfeit marble that weighs 9 and another counterfeit marble that weighs 11. If you can only use the scale twice, what is the maximum number of marbles you can have, where you would be guaranteed to identify the light and heavy marble?
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12. howardl1963 added a post in a topic

I'm not in love with my solution, but I think this works.

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13. howardl1963 added a post in a topic

That's a truly elegant solution. Quite impressive. When you consider how prosaic and one dimensional my solution is compared to yours, it seems weird that your solution is only 5.5% better.
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14. howardl1963 added a post in a topic

Thanks for a very interesting puzzle bushindo. I've thought about this one for awhile and the best I can do is a little over 71%. I'll be very curious to see how you get to over 75%.

First an observation on the puzzle and puzzles of this nature:

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15. howardl1963 added a post in a topic

They are not allowed to communicate their order in any way, other than looking at their respective hats once the game starts. So, they are only allowed to develop a strategy ahead of time that takes into account the hat numbers and who those hats are on. Any other info, like lining up in order, or winking at each other etc. is not allowed.
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