<ontadian@hotmail.com> wrote in message news:26906479.1175298715649.JavaMail.jakarta@ nitrogen.mathforum.org... > I would be interested to know if there is an answer to the following:- > If a wooden stick is broken randomly into six pieces what is the probability that a a skeletal regular/irregular tetrahedron could be formed from the six pieces ? Hi Ontadian! My bet is around 0.0655. But I have no smart solution, only brute force. One million sticks each marked randomly in 5 places and cut assemble the 6 pieces in 30 combinations and see if one of them has a volume, check http://en.wikipedia.org/wiki/Tartaglia and then hope to have made no errors! Is the number about what you expected? Greetings Hans.

<ontadian@hotmail.com> wrote in message news:12035475.1176472753296.JavaMail.jakarta@ nitrogen.mathforum.org... > Hi Hans, > This is not really my area of knowledge, but it does seem that the "method" of breakage would alter the probability figure. If we were to start with consecutive pieces broken off, then at each breakage, would not the probability be .5 thus making the end result .5^5 or .03125 ? But at some point would the .5 value not apply ? > Regards > Bill Hi Bill, yes, breaking in that way would alter the probability. There would be more small pieces, and the probability would drop. Sure enough, repeating the run of 1 million sticks, broken like you say, gave a probability of 0.0077, with all reservations, of getting a set of pieces that could form a tetrahedron. Accuracy about 1 on last digit. Complicated problem! Regards, Hans.