Question

I have an octahedral die, that is, a symmetrical object with eight faces. Each face has a different number marked upon it. If I roll the die and tell you what number comes uppermost, how many bits of information have I given you?

Answer 1

Rolling an octahedral die with eight faces and communicating the outcome provides 3 bits of information, as there are eight possible outcomes and the number of bits is found using the logarithm base 2 of the number of outcomes.

Step-by-step explanation:

When rolling an octahedral die, with each of its eight faces having a unique number, you are essentially choosing one outcome from eight possible outcomes. To determine the amount of information given when you roll the die and communicate the number that lands face up, we can use the concept of bits from information theory. One bit can encode two distinct outcomes (as in a binary system with 0 and 1). The number of bits (b) needed to represent a number of outcomes (n) can be calculated using the logarithm base 2: b = log2(n).

In the case of an octahedral die, we have eight possible outcomes, so the calculation would be b = log2(8) which equals 3. Therefore, rolling an octahedral die and telling someone the number that comes uppermost gives them 3 bits of information.