Question

If you have 20 dice (with 6 faces each), how many different numbers can you create putting the dice in one line and interpreting each face as a digit?

Answer 1

`6^20`
(a big number: according to my calculator in the order of `3.65616xx10^15`)

Explanation:

There are 6 different possible first die values; each of these gives a different number.
So the number of different numbers you can get with 20 dice is:
`color(white)("XXX")6 xx`the number of different numbers you can get with 19 dice

Similarly the number of different numbers you can get with 19 dice is:
`color(white)("XXX")6 xx` number of different numbers you can get with 18 dice
or
The number of different numbers you can get with 20 dice is
`color(white)("XXX")6 xx 6 xx` number of different numbers you can get with 18 dice.

Continuing this pattern, we see that
the number of different numbers you can get with 20 dice is
`color(white)("XXX")6 xx 6 xx 6 xx ...` for a total of 20 times
or
`color(white)("XXX")6^20`