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Mysterious Journey II Hints
Let's try using the decimal way.
1 of 18: First, let's convert the two base-12 numbers to decimal.
2 of 18: Remember that the left-most digit represents 12 times 12 times 12. And in the number 3468, there are 3 of those. That's 5184.
3 of 18: The second digit represents 12 times 12, and in the number 3468, there are 4 of those. That's 576. Added to the 5184 (from the first digit), we have a "running total" of 5760.
4 of 18: The third digit represents 12, and in the number 3468, there are 6 of those. That's 72. Add it to the 5760 to make our "running total" 5832.
5 of 18: Finally, the last digit represents "ones" -- or, itself. That's an 8, in our example. Add it to 5832 to get a final conversion total of 5840.
6 of 18: Now we convert the second base-12 number (8041) to decimal in the same manner: 12 * 12 * 12 * 8 = 13824 12 * 12 * 0 = 0 12 * 4 = 48 1 = 1 Add those together to get 13873.
7 of 18: Summing the two decimal numbers results in 5840 + 13873 = 19713. Now we have to convert that back to base 12. (Here's where it gets a bit sticky.)
8 of 18: The first digit of our answer, as we said earlier, represents groups of 12 * 12 * 12 -- or 1728. How many "1728"s are there in 19713?
9 of 18: The answer is 11 -- which is the largest number of times that 1728 will divide into 19713.
10 of 18: What is left, after accounting for "eleven 1728's"?
11 of 18: 11 * 1728 = 19008. And 19713 (our original number) minus 19008 (which is the value of the first digit) is 705. So the last three digits of our code must equal 705.
12 of 18: The second of the four digits in our resultant answer represents 12 * 12 -- or 144. How many "144"s are there in 705?
13 of 18: The answer is 4 -- which is the largest number of times that 144 will divide into 705.
14 of 18: What is left, after accounting for "four 144's"?
15 of 18: 4 * 144 = 576. And 576 from the remaining 705 would leave 129 for the final two digits.
16 of 18: The third of the four digits in our resultant answer represents the "twelves" place. How many "12"s are there in 129?
17 of 18: That one should be pretty easy -- there are 10 "12's" in 129, with 9 left over. So we immediately have the last two numbers of our answer: 10 and 9.
18 of 18: Therefore, the four base-12 numbers in our solution are 11, 4, 10, and 9.
