The price of a 6.5oz bottle of Coca Cola stayed fixed at 5c from 1886 to 1959. Daniel Levy and Andrew Young document this fact and ask why this might have been the case in a period that saw two world wars and the Great Depression.  They offer two technological explanations for price rigidity:

First, we demonstrate that an installed base of vending machines with nickel-only capability, and the
evolution of the technology that could accommodate multiple type coins and change making,
imposed an important constraint on the ability of the Coca-Cola Company to adjust the Coke’s
price. Second, at the 5¢ price per serving, the smallest price increase compatible with the
consumer still using a single coin was a 100 percent jump to 10¢. A monetary transaction
technology for smaller price adjustment while keeping consumer “inconvenience costs” low in
terms of the number of coins needed for purchasing a bottle of Coca-Cola, was not available.

How can you get around these technological constraints?

You could lobby your friends:

Woodruff [Coca Cola CEO] submitted a request in 1953 to the newly elected President Dwight Eisenhower (his hunting companion and friend) himself, to get the U.S. Department of Treasury mint a new 7 1/2-cent coin.
Eisenhower forwarded the request to the Treasury Department officials who did not like the idea.

Or ingeniously in an early example of mechanism design, you could randomize bottle delivery while retaining the nickel technology in the vending machine:

“Instead of offering one ‘Coke’ for 6¢ the coin cooler offers 8 ‘Cokes’ for 45¢,
which is only 5.625¢ (5 5/8¢) per bottle. [The] coin cooler [delivers] either an
empty bottle or no bottle at all for one nickel in every nine deposited. This
absence of ‘Coke’ is called an official blank. Please be warned that, if you fail to
deposit nine nickels, at worst you will strike the blank and have to deposit
another nickel for your ‘Coke.’ At best you will miss the blank (8 times out of 9)
and your ‘Coke’ will cost only a nickel, but as stated, on the average ‘Coke’ sells
for 5.625¢ per bottle—the only price at which it is offered”

The plan might actually have been tried out in Chicago and Canada!

(Hat Tip: Tilman Klumpp and Xuejuan Su)