Here is a square sequence of numbers.
392?
6 3
7 4
?817
What are the two question marks?
(In reply to
re(2): Solution by SilverKnight)
And in Gamer's vein, let's take a look at his observation and see what we find...
Note that... you can start with any two digit number (from 00-99), and generate one of these patterns. It *will* cycle (eventually). Here are the cycles:
Period 1:
0
Period 3:
550
550 (can't divide the period in half, showing it a 2nd time)
Period 4:
26
84
Period 12:
392134
718976
Period 20:
4606628088
6404482022
Period 60:
325729101123583145943707741561
785381909987527965167303369549
________
The sequence that corresponds to the puzzle has period 12, but this puzzle could have easily used one of these other sequences
Note that I split each one in half lining up opposing numbers (to demonstrate that opposing numbers all add up to 10)
Also note that the period = the number of digits in the string = the number of two digit combinations that exist in that sequence... therefore,
If you sum the periods of each sequence, they add up to 100. 1 + 3 + 4 + 12 + 20 + 60 = 100 (If you don't like 00, then just include (01-99) and eliminate the sequence with period 1.) and
This makes sense since each number (00-99) will generate the whole sequence to which it belongs (e.g., if I start with 63, or 39, or 92, or 47, I will generate the sequence with Period 12). Each two digit number can generate one and only one sequence. And all two digit numbers will generate a sequence.
____________
Okay enough analysis on this puzzle for a while... who's taking it from here?
re(3): Solution (further analysis)
