You have a bucket of 12lbs of a mixture of dry chemicals including both powders and coarse agglomerates. You actually need a 4.5lb sample. The rest will be desposed of.
You pour the sample into your other bucket and notice a serious issue: when such samples are poured from one container to another, they segrate by particle size to some random extent. In this case, the largest chunks poured first so the 4.5lb sample is far coarser than that remaining in the original bucket.
You find a Riffle-type splitter which is designed to split any material poured into it into two identical size samples with the same particle size distribution. This splitter, however, only can deposit the material into two tins which can only hold 1 lb each. If you let the sample pour onto the floor (no tin) the sample will be contaminated. Note: this means that you can only pour 2lbs at a time into the splitter but both 1lb tins it fills will have the sample distribution.
What is the minimum number of tins you need in order to get your sample? What is the minimum number of splits to get your sample with this many tins (to reduce splitting error)?