Calculator Display
A calculator has an eight-digit display and a decimal point that is located at the extreme right
of the number displayed, at the extreme left, or between any pair of digits. The calculator can
also display a minus sign at the extreme left of the number. Example: 1234.5678
and 1234.5678
How many distinct numbers can the calculator display?
Find a pattern and an explicit formula.
What would be the answer for a calculator with a 10-digit display?
Here's a way to begin with displaying only one digit displayed; an underscore is where a digit
would appear, and a period
( . ) is where the decimal point could be located.
Let's begin by counting zero only once. We'll add one to our final talley.
One digit display:
Case A:
._
The digits that can occupy this position are 1-9
Case B:
_. The digits that can occupy this location are 1-9
AND each of these cases can be negative.
Two digits display:
Case A:
._ _ The digits that can occupy first position are 0-9 and second position 1-9
Case B:
_._
Case C:
__.
AND each of these cases can be negative