Moderator: Flannel Jesus
James S Saint wrote:The very first thing that threw me off was that I was concerned about the order of the numbers proposed, later deciding that they weren't bothering with which order, but merely which two numbers.
Carleas wrote:James S Saint wrote:The very first thing that threw me off was that I was concerned about the order of the numbers proposed, later deciding that they weren't bothering with which order, but merely which two numbers.
Sauwelios wrote:
Carleas wrote:That's the one, Phoneutria.
Here's another I just came across, I haven't had time to try to figure it out but it looks like fun, and mathier than most problems of this kind.Sasha Volokh wrote:Two numbers a and b are between 2 and 99. [Note: They’re not constrained to be different from each other. [S.V.]]
Peter is given the product of the numbers, ab (and knows he is given the product).
Sarah is given the sum a+b (and knows she is given the sum).
They also know the numbers are between 2 and 99.
They are UVa math majors, so they are great at math and completely honorable!
Peter says, “I don’t know the numbers.”
Sarah says, “I knew you didn’t know the numbers.”
Peter then says, “I know the numbers now.”
Sarah then says, “Ah ha! I know the numbers now.”
What are the numbers?
This one could take a while.
Lev Muishkin wrote:
Lev Muishkin wrote:Sauwelios wrote:
Prime numbers between 3 and 99:
5 7 11 13 17 19 23 29
31 37 41 43 47 53 59 61 67 71
73 79 83 89 97
Why can't they be prime?
Carleas wrote:James S Saint wrote:The very first thing that threw me off was that I was concerned about the order of the numbers proposed, later deciding that they weren't bothering with which order, but merely which two numbers.
phoneutria wrote:I think that there might be a way to narrow the pool of numbers to a much smaller amount right from the start. I'm brushing up on my number theory, haven't played with any of this in over 10 years
James S Saint wrote:More than the Sum of Its Parts
Just think about it.
Count them.
Alice at the Convention of Logicians:
At the Secret Convention of Logicians, the Master Logician placed a band on each attendee's head, such that everyone else could see it but the person themselves could not. There were many different colors of band.
The Logicians all sat in a circle, and the Master instructed them that a bell was to be rung in the forest at regular intervals: at the moment when a Logician knew the color on his own forehead, he was to leave at the next bell. They were instructed not to speak, nor to use a mirror or camera or otherwise avoid using logic to determine their band color.
In case any impostors had infiltrated the convention, anyone failing to leave on time would be gruffly removed at the correct time. Similarly, anyone trying to leave early would be gruffly held in place and removed at the correct time.
The Master reassures the group by stating that the puzzle would not be impossible for any True Logician present. How did they do it?
Return to Science, Technology, and Math
Users browsing this forum: No registered users