Posted on Categories data science, Mathematics, Statistics, Tutorials2 Comments on Imputing Out of Mixtures, or Un-Stirring Spicy Soup

## Imputing Out of Mixtures, or Un-Stirring Spicy Soup

Here is a fun combinatorial puzzle. I’ve probably seen this used to teach before, but let’s try to define or work this one from memory. I would love to hear more solutions/analyses of this problem.

Suppose you have `n` kettles of soup labeled `0` through `n-1`. For our problem we assume that `k` kettles of soup are extremely spicy. We want to figure out which kettles contain spicy soup.

Image source: Mad Dog 357 / Amazon

This presents an interesting puzzle when `k` is much smaller than `n`. We are assuming that spicy is a rare event we want to detect. We are also assuming the spicy soups are so spicy, that they remain spicy even when combined with other soups. So when we prepare mixtures of soups we experience the union of the spiciness of the included soups.

The question is: if we prepare tasting bowls that are mixtures of samples from the kettles- how many bowls do we have to prepare to reliably identify all of the spicy soup kettles? This is hopefully in the spirit of the “counterfeit gold coin puzzle” as seen in the Columbo detective show (though I end up using a bit more math).

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## Unspeakable bets: take small steps

I was watching my cousins play Unspeakable Words over Christmas break and got interested in the end game. The game starts out as a spell a word from cards and then bet some points game, but in the end (when you are down to one marker) it becomes a pure betting game. In this article we analyze an idealized form of the pure betting end game. Continue reading Unspeakable bets: take small steps

Posted on Categories Expository Writing, Mathematics