1 2 3 4 5 6 7 8 9
1 4 9 6 5 6 9 4 1
1 8 7 4 5 6 3 2 9
1 6 1 6 5 6 1 6 1
Above are 4 related sequences, each with 9 digits. What would happen if each sequences continued beyond the 9th digit?
Where do these sequences come from? What would the 5th, 6th and 7th sequences look like ?
The second and 4th sequences are symmetrical but not the 1st and 3rd ones. Why ?
There are many more sequences that can be created as the one's above are. What would you these look like?
Diagonals
I spotted that the NW-SE diagonals all follow a pattern: In the first one - 1476 - the first and third are odd. In the second one - 2941 - the odd numbers are the second and forth. In the third it is the first and third again, and in the forth it is the second and forth again. This will continue as long as the pattern is. Also, all columns add up to numbers divisible by 4.
DIAGONALS, COLUMN TOTALS & HINTS
Thanks for responding, Brian .
First note correction to sequence 4 in the Challenge.
DIAGONALS
The odd-even pattern is because each sequence has the same odd-even pattern.
COLUMN TOTALS
4 20 20 20 20 24 20 20 20
If you add a column before the first one and 10 more afterwards the column totals would be
[ 0 ] 4 20 20 20 20 24 20 20 20 [ 0 4 20 20 20 20 24 20 20 20 ]
What does these column totals suggest ?
What sequence starts 1 4 9 .... ?