What is this problem and where did I find it?
- From: achava@xxxxxxxxxxx
- Date: 27 Jun 2005 15:55:42 -0700
I have been sharing some math problems with friends and one of them
went something like this:
You have a calculator with 0 in the display, and the only keys that
work are the sin, cos, tan, arcsin, arccos, and arctan keys. Prove
that you can obtain any rational number (?) assuming that the
calculations are done with absolute accuracy and that you can display
an arbitrary rational number.
I am not sure that this is the correct statement of the problem.
Please let me know the correct statement of the problem and, if you
know, where on the web I found it.
In return I offer you a problem that comes from Martin Gardner's column
in Scientific American from a long time ago:
Come up with a 10 digit number (base 10) with the property that the
left-most digit tells the number of 0's in the whole number, the next
digit over tells the number of 1's, ..., the last digit tells the
number of 9's in the whole number.
Note that if I posed the problem in base 4 rather than in base 10, an
answer would be 2020 since it has 2 0's, 0 1's, 2 2's, and 0 3's.
To make this problem considerably more interesting, find all solutions
to this problem for every base n. I will mention that for some value a
< 10, there is a unique solution for every base b > a.
If anyone is interested I will either drag out or recreate my solution.
Regards,
Achava
.
- Follow-Ups:
- Re: What is this problem and where did I find it?
- From: achava
- Re: What is this problem and where did I find it?
- From: Gerry Myerson
- Re: What is this problem and where did I find it?
- From: Ted Hwa
- Re: What is this problem and where did I find it?
- Prev by Date: Re: f = f(x, y)
- Next by Date: Re: Orlow cardinality question
- Previous by thread: transitive, antisymmetric and symmetric, but neither reflexive, nor reflexive,
- Next by thread: Re: What is this problem and where did I find it?
- Index(es):
Relevant Pages
|
Loading
