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?

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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?

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Answer 1 · 2016-01-14T17:13:43

$6^{20}$ $6^20$
(a big number: according to my calculator in the order of $3.65616 \times 10^{15}$ $3.65616xx10^15$ )

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:
$XXX 6 \times$ $color(white)("XXX")6 xx$ the number of different numbers you can get with 19 dice

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

Explanation:

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