What is the herfindahl–hirschman index (hhi) of a pure monopoly?

Answer;
In a pure monopoly the HHI is 10,000.
That is, if one largest firm has 100% of the market share for the case of a pure monopoly , then HHI will be; 100 ² = 10,000

Explanation;
The Herfindahl-Hirschman index is a common measure of market concentration that is used to determine market competitiveness, often pre and post M & A transactions. Calculated by squaring the market share of each firm competing in a market and then summing the resulting numbers. 
A pure monopoly is where a single firm is producing a product or a service for which there are no close substitutes. 

Sugar + oxygen > carbon  dioxide + water + energy  c6h1206 + 6o2 > 6co2 +6h2o + energy  and the numbers after the element symbols are small.