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#1 2012-10-05 10:29:58
- MathsIsFun
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New Puzzles 4
Even more "Stephen Froggatt" puzzles::
Pet Show
Newspaper Caper
Three Of The Best
A Brave Puzzle
A Weighty Problem
The Make-You-Very-Cross Number
NIM-ble Thinking
MatheMusic
A Hole New Board Game
Matches Of The Day
Ancestrally Speaking
Have You Herd Of Cows
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#2 2012-10-05 17:21:44
- bob bundy
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Re: New Puzzles 4
hi
Sorry ... bit of a rush.
Weighty Puzz think I have another soln.
More later
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2012-10-05 18:00:32
- bobbym
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Re: New Puzzles 4
Hi MIF;
Funny that Bob and I went for the same problem.
For the weighty problem there are 10 solutions to the problem. Not counting permutations. Want to add the rest? Hope I did not prune out any others.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2012-10-06 11:55:05
- MathsIsFun
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Re: New Puzzles 4
Great! I will put that in the solution.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#5 2012-10-06 19:03:01
- bobbym
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Re: New Puzzles 4
Hi MIF;
A mathematical solution would be nice but I do not have one.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2012-10-07 03:57:19
- anonimnystefy
- Real Member
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Re: New Puzzles 4
I would think there is one, thought it does seem GFs might be of use.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#7 2012-10-07 07:29:21
- bobbym
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Re: New Puzzles 4
Hi anonimnystefy;
GF's usually count the number of solutions not the type of solutions. For that, I usually call on number theory.
Still in all a gf played an important part in the program. Without it there would be no program.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#8 2013-03-04 23:04:21
- Thurhame
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Re: New Puzzles 4
There is a problem with the "Three Of The Best" puzzle.
The puzzle claims there are two solutions to "1+(1/(1+(1/...)))". However, it actually converges to the golden ratio
MORE COMPLEX PROOF:
The formula is the limit as n goes to infinity of the sequence defined by .
Assume some exists (otherwise the sequence would be undefined).
Define a sequence .
We proceed by induction.
Base step:
Inductive Hypothesis:
Thus we have proved by induction the relation for all .
Since is a sequence of the form , this ratio converges to the golden ratio.
Last edited by Thurhame (2013-03-06 12:28:02)
#9 2013-03-04 23:15:36
- Agnishom
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Re: New Puzzles 4
Wonderful, Thanks!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#10 2013-03-05 01:39:19
- anonimnystefy
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Re: New Puzzles 4
Hi Thurhame
Can you specify where it was claimed that 1+1/(1+1/(1+...)) is equal to 2?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#11 2013-03-05 03:24:55
- bobbym
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Re: New Puzzles 4
Hi;
The answer given is 2 when it should be the golden ratio.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#12 2013-03-05 04:23:07
- Thurhame
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Re: New Puzzles 4
anonimnystefy wrote:
Hi Thurhame
Can you specify where it was claimed that 1+1/(1+1/(1+...)) is equal to 2?
Oh, my mistake, it just said there were two solutions to the formula. However, that's still wrong; my proof shows that any solution must be equal to the golden ratio, i.e. there are at most 1 solutions.
Edited my post above. Thanks!
Last edited by Thurhame (2013-03-05 04:26:01)
#13 2013-03-05 05:30:13
- anonimnystefy
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Re: New Puzzles 4
Hi Thurhame
Yes, with that I agree. The answer should be one. I think they didn't consider that the number must be positive.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#14 2013-03-06 12:27:40
- Thurhame
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Re: New Puzzles 4
Ah, thanks for reminding me, my simple less-rigorous proof isn't adequate if i'm only proving the number of solutions, rather than the value. Removing it now. Hope the more complex proof doesn't make anyone's eyes glaze over.