Xi'an's Og

A form of Bernoulli factory with limited energy from The Riddler: being given the choice of 0<p<1, what is the minimal number n of throws such that the outcomes of n iid B(p) draws can be partitioned into six groups of equal probability? Running a brute force R code [in the train to Cambridge] and checking random partitions for different values of p and n, I found a near fit for n=6 and p around 0.42. With partition weights

0.1658159 0.1669405 0.1657981 0.1662112 0.1682599 0.1669745

while missing the n=5 case for p≈0.3034.

This entry was posted on May 23, 2023 at 12:23 am and is filed under Books, Kids with tags Bernoulli factory, mathematical puzzle, The Riddler. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.