testing image postingThis problem had me laying in bed awake, so I wrote a MC. I think the thief would want to watch the guard for a long time and build a histogram of the time between guard visits, and then from this histogram he can calculate the probability of a successful attempt as a function of how long it has been since the guard last passed by. The following is for a guard doing a pattern of:clockwise X * RAN(0->1), counter-clockwise X * RAN(0->1), .... with X=200 secondsCalling this distribution H(t), then the probability of a successful break-in attempt isP(t) = sum[ H(t+300)->H(t+inf) ] / sum[ H(t)->H(t+inf) ] Then I scan through a couple of values for X. Some structure develops in the distributions. I see that for this movement function the optimal value of X is 360 seconds, which is the time to go around one time.Here is X = 300 sec: Inflections appear at 60 and 360 seconds. An edge develops after 360 seconds in the time distribution: I think the edge after 360 is from sequences of 3 movements that go all the way around (the guard passes by going the same direction as the previous time). Prior to 360 seconds, if the guard comes back he'll be coming opposite the direction.At X=400, there is a new feature, a spike at t=360 seconds. This is from the single movements that are > 360 seconds.The probability curve has become discontinuous: The thief's best chance is to wait 60 seconds after the guard passes, then begin his attempt. This minimizes the chance that the guard will turn around and catch him. If he waits longer than 60 seconds he is vulnerable to the guard going all the way around and catching him.At X=500 there is a new edge in the time distribution at 720 seconds:I think this edge is from sequences of 2 movements. All of the 2 move sequences that generate a delta T measurement will be constrained to to occur with delta T < 720 seconds.Empirically probing the probability curve as a function of X, X=360 seconds minimizes the thief's success for the given movement pattern:X=360It seems like the thief's algorithm can be improved by including the time of the second to last passing also. This would give you information about how long the guard is can be expected to travel before turning around.side note:The structure at X>800 seconds is noise. The summing procedure creates the structure; if the MC is repeated, a different structure will appear:X=360

posting image answering

is there a forum for testing?

Not really. This seems as good a place as any.P.S. image http://i761.photobucket.com/albums/xx25 ... b200-1.jpg isn't coming through.

If this is for farmer's dog track security guard thread in brainteasers, then you can either quote from here and paste over there, or leave your images here and just link to this thread from there.

Matrix - What is RealThe Architect Speech The ArchitectQuoteYour life is the sum of a remainder of an unbalanced equation inherent to the programming of the matrix. You are the eventuality of an anomaly, which despite my sincerest efforts I have been unable to eliminate from what is otherwise a harmony of mathematical precision. While it remains a burden to sedulously avoid it, it is not unexpected, and thus not beyond a measure of control. Which has led you, inexorably, here.It is confusing because so much information is given in such a short period of time.QuoteResidual Self Image: Mental Projection of your Digital SelfWhat Is Real ? How do you define real, if you talking about you can feel, smell, taste and see, then real is simple electrical signals interpreted by your brain

QuoteOriginally posted by: kwd1testing image postingThis problem had me laying in bed awake, so I wrote a MC. I think the thief would want to watch the guard for a long time and build a histogram of the time between guard visits, and then from this histogram he can calculate the probability of a successful attempt as a function of how long it has been since the guard last passed by. The following is for a guard doing a pattern of:clockwise X * RAN(0->1), counter-clockwise X * RAN(0->1), .... with X=200 secondsCalling this distribution H(t), then the probability of a successful break-in attempt isP(t) = sum[ H(t+300)->H(t+inf) ] / sum[ H(t)->H(t+inf) ] Then I scan through a couple of values for X. Some structure develops in the distributions. I see that for this movement function the optimal value of X is 360 seconds, which is the time to go around one time.Here is X = 300 sec: Inflections appear at 60 and 360 seconds. An edge develops after 360 seconds in the time distribution: I think the edge after 360 is from sequences of 3 movements that go all the way around (the guard passes by going the same direction as the previous time). Prior to 360 seconds, if the guard comes back he'll be coming opposite the direction.At X=400, there is a new feature, a spike at t=360 seconds. This is from the single movements that are > 360 seconds.The probability curve has become discontinuous: The thief's best chance is to wait 60 seconds after the guard passes, then begin his attempt. This minimizes the chance that the guard will turn around and catch him. If he waits longer than 60 seconds he is vulnerable to the guard going all the way around and catching him.At X=500 there is a new edge in the time distribution at 720 seconds:I think this edge is from sequences of 2 movements. All of the 2 move sequences that generate a delta T measurement will be constrained to to occur with delta T < 720 seconds.Empirically probing the probability curve as a function of X, X=360 seconds minimizes the thief's success for the given movement pattern:X=360It seems like the thief's algorithm can be improved by including the time of the second to last passing also. This would give you information about how long the guard is can be expected to travel before turning around.side note:The structure at X>800 seconds is noise. The summing procedure creates the structure; if the MC is repeated, a different structure will appear:X=360you posting this from prison ?