Re: The Harem-problem

Hi,


Your formula seems to hold against the values I calculated with this simulator. Could you explain how you came up with it?


Regards,
Frank.

matt271829-news@xxxxxxxxxxx wrote:

On Jan 28, 8:52 am, Frank Cornelis <i...@xxxxxxxxxxxxxxxx> wrote:
Hi,

When I was still a student I came up with a problem I called the
Harem-problem. The problem goes like this (sorry if I offend some
people, but it's an interesting mathematical quest): how many women does
a man need to be able to 'do it' every day of the month, and this with a
given probability?

I started solving this probability problem but never found a closed
formula for it. The document can be found at:http://www.frankcornelis.be/conqueror.pdf

Can anyone give any hint on how to continue the work?

Unfortunately I can't read Dutch(?), but your question started me thinking so I made some assumptions about what you're trying to do based on other people's replies and some of the diagrams in the paper. (Though looking at the length and complexity of your paper I wonder if my assumptions might be way off beam and way too simple).

Anyway, I assumed n women, each with a monthly cycle of t days, with each woman unavailable for a block of b consecutive days within that cycle, the blocks being uniformly randomly distributed. Provided t >= 2*b (which seems reasonable!) I make the probability that there will be at least one day in the cycle when all women are unavailable equal to (b^n - (b - 1)^n) / t^(n - 1). If t < 2*b then an adjustment is needed, but I have not tried to work out that case.

.

Relevant Pages

  • Re: Einsteins Doppler equation wrong?
    ... :>> cycle." ... :>> I was running a test procedure on the Harrier simulator with A ... and maximized when E is at zero, ... to those retarded integrals some of us need to struggle so hard to ...
    (sci.physics.relativity)
  • Re: Superscalar Out-of-Order Processor on an FPGA
    ... I'm unfamiliar with cycle C, but your post has me interested. ... Is this a specific simulator? ... Verilog because it is fairly close to C syntax but the semantics ... Cycle C simulations can run models many orders fasters than HDL ...
    (comp.arch.fpga)
  • Re: difference between formal and functional verification
    ... that I had a second question, about cycle besed semantics ... the same functional verification or formal verification. ... Even if a signal should change its value between active clock edges the ... simulator changes its value at the preceding ...
    (comp.lang.verilog)
  • Re: Cycles in a random bijective mapping
    ... For your random bijective mapping, ... probability of encountering a cycle after taking x steps is floor(x/c, ... There is a probability /n that element 0 maps to some other ...
    (sci.crypt)
  • Apple II Simulator
    ... develop Apple II Simulator which it runs accuracy than Apple II Emulator. ... The fact is that I am very interested to study simulator, ... I have discussed earlier to record nanoseconds each cycle which it ...
    (comp.sys.apple2)