Why is Christmas the same day as Halloween?

Because in Decimal (Dec, also short for December), we count units (ones) on te right hand column, then 10s to the left of that (then hundreds, thousands, etc, as we go further left). But in Octal (Oct, also short for October), we count units (ones) on the right hand column, then 8s, then 64s, 512s, and so on - multiplying by 8, rather than 10, every time.

So in Base 10, Decimal, "25" means "(2 x 10) + (5 x 1)" but in Base 8, Octal, "31" means "(3 x 8) + (1 x 1)".

3 x 8 = 24, and 1 x 1 = 1, so "Oct 31" is "Dec (24+1)" which is "Dec 25"

You can also convert between bases in the Bash shell; if you've declared HALLOWEEN to be a decimal integer (with the "declare -i HALLOWEEN") command), then "HALLOWEEN=8#31" won't set it to that literal string, but will instead set it to the value of "31" in Base 8:

$ declare -i HALLOWEEN
$ HALLOWEEN=8#31
$ echo $HALLOWEEN
25
$ 

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