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?

1 Answer
Jan 14, 2016

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