## stack overload

**T**he Riddle this week is rather straightforward to explain: stacking identical objects (bars of length and mass two, say) on top of one another so that the center of each new bar is uniformly distributed along the previous bar, what is the distribution of the number of bars when the stack collapses? If I am not confused, the stack collapses the first time the centre of gravity of an upper stack leaves the interval represented by the bar just below. Namely

when the *x _{i }*are the bar centres, or equivalently

where the ε_{_i}‘s are U(-1,1). Which is straightforward to code in R by looking at means of cumulated sums.

March 8, 2021 at 6:10 pm

How about a variant: what’s the maximum allowable offset to guarantee the tower never collapses? Consider the related game where you stack blocks (or playing cards) until the top one lies entirely outside the location of the first one. In that game, the cards’ positions follow a log curve when the number of cards required is a minimum.

March 9, 2021 at 3:44 pm

Thanks : I think this variant is more “classical”, unless I misunderstand the constraint.

March 4, 2021 at 8:11 am

[…] article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here) […]