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The QWERTY layout was created by Milwaukee, Wisconsin newspaper editor Christopher Latham Sholes, who began experimenting with various keyboard designs in the 1860s including a layout with only two rows of keys. By April 1870, his keyboard resembled the modern QWERTY layout with four rows of keys and when Sholes' design was sold to Remington in 1873, it looked like this (on the right is today's layout):
Sholes excluded the 0 and 1 to because they were deemed redundant seeing as they could be represented with the letters O and I, which also simplified the layout and cut manufacturing/maintenance costs.
Although Sholes made further changes to his design in the following years, a patented version from 1878 hadn't yet added the numbers 0 and 1, but he did find better positions for the period and ampersand.