Practice problem
What Is a Combination?
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The sound made when you press a key on a telephone's dialing pad is made up of two pure frequencies, played at the same time. Each row and each column has its own frequency with each button being composed of the intersection of those two frequencies. For example, when you press "2", you hear 697 Hz and 1336 Hz, like two horns each playing a different note at the same time. Our phones use a total of 7 different frequencies, taken in different pairs, to represent the digits 0-9.
What is the minimum total number of frequencies that one could use to design an alternative system, in which each digit from 0 to 9 is represented by some pair of frequencies, but does not have to be tied to rows or columns?