At an early age, Willgodt worked at a lamp store and then for an instrument maker before studying mechanics.
However, Sweden’s dire economic situation prompted him to leave for Russia in 1868. There he began to work on his arithmometer. He also worked for the Expedition before starting his own paper-cutting business.
In 1882, he designed a turnstile for controlling ticket sales and in 1887 began producing his own arithometers. As demand grew he found the Mechanical Factory of Odhner & Hill, and eventually became wealthy. His calculators would be produced until the 1970s.
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