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
Alan P.
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#

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