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Mysterious Journey II Hints
Arithmetic in Base 12
1 of 5: Arithmetic in base 12 works on the same principles as in our decimal system -- or any other similar system, for that matter. Adding two numbers can still be done by adding the columns, and "carrying" to the next column to the left, when necessary.
2 of 5: In base 10 (our usual counting system) 6 plus 6 equals twelve, which would be written as "12" (one group of ten, plus two "ones"). Adding 6 plus 6 in base 12 still has a value of twelve, but would be written as "10" (the "1" in this example stands for one group of 12). Remember, counting in base 12 looks like this: 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, 10 (where "a" has a value of ten; and "b" has a value of eleven).
3 of 5: The system of adding and carrying groups of twelve can also be used on more complicated addition equations. The difficulty is in remembering when to carry a number over from the "ones" column to the "twelves" column.
4 of 5: For example, to see again how to carry groups of twelve over to the "twelves" column (instead of groups of ten to a "tens" column), we'll add 37 and 46 in base 12. In base 12, adding the "7" and the "6" results in thirteen -- but it is not written "13", instead it is written "11". The "1" on the left represents one group of "twelve" (carried over to the "twelves" column) and the "1" on the right is just "one". The next step is to add the "twelves" column -- "3" plus "4" plus the "1" carried over to the "twelves" column, resulting in "8". The total is written as "81" -- which means there are 8 groups of twelve plus 1.
5 of 5: Remember that "37" and "46", in base 12, do not have values of thirty-seven and forty-six. The three (in 37) is in the "twelves" column, plus seven "ones" (i.e., 43); the four (in "46") is in the "twelves" column, plus six "ones" (i.e., fifty-four). Adding those two decimal numbers (43 and 54) results in 97 decimal -- which is precisely what "81" represents in base 12 (eight "twelves" plus one "one").
