Morning Daydreams

I've been daydreaming about chess. I like to try to hold a vision of it in my mind and keep track of the movements of the pieces on it. In a way, it's sort of a memory exercise. How long can I keep an imagined game going before I lose track of which piece is where?

Lately, I've been dividing it up into a handful of basic games. In some, I start with the classic opening maneuver of putting my knights out front. In others, I might start out by moving a pawn forward to liberate a Bishop. In the same game, perhaps I'll start a "pawn assault" on the opposite side of the board. Therefore, it sounds like it might be hard to remember where all of the pieces are on the board, but you eventually start to crystallize how a particular game might go, at least at the outset.

However, I still haven't managed to play through a game yet before drifting off into other topics. Yesterday morning, I started thinking about the number seven. Did you know that, for any multiple of seven, you can play with the numbers in each place and come up with other multiples of seven?

7: 7-0=7 and 7-7=0. From 7, 0: 70. 70/7=10

14: 7-1=6 and 7-4=3. From 6, 3: 63. 63/7=9

21: 7-2=5 and 7-1=6. From 5, 6: 56. 56/7=8

28: 7-2=5 and 8-7=1. From 5, 1: 51. NON-DIVISIBLE BY 7 and PRIME

35: 7-3=4 and 7-5=2. From 4, 2: 42. 42/7=6

42: 7-4=3 and 7-2=5. From 3, 5: 35. 35/7=5

49: 7-4=3 and 9-7=2. From 3, 2: 32. NON-DIVISIBLE BY 7 and =2^5

56: 7-5=2 and 7-6=1. From 2, 1: 21. 21/7=3

63: 7-6=1 and 7-3=4. From 1, 4: 14. 14/7=2

70: 7-7=0 and 7-0=7. From 0, 7: 7. 7/7=1

Therefore, I have a clear progression except in two cases. Doing the operation on the other ones gave me the pattern you see above, from 10 to 1. I were to apply the technique used on the others, I would get the numbers 51 for the first and 31 for the other. That just wouldn't work. However, let me try something weird real quick.

12-7=5 and 18-7=11. From 5, 11: 61. Now let's do a decimal reflection:

61: 10-6=4 and 10-1=9. From 4, 9: 49. 49/7=7

Hmm...

49: 14-7=7 and 19-7=12. From 7, 12: 82 Gonna have to do something a little different here

82: 10-8=2 and 20-12=8. From 2, 8: 28. 28/7=3...HAD TO GO UP

Now that's interesting. Look at how that fits right in with my progression. However, I wonder if that's a valid method for all of the other combinations. Let's try.

21: 12-7=5 and 11-7=4. From 5, 4: 54

54: 10-5=5 and 10-4=6. From 5, 6: 56. SAME RESULT as by ORIGINAL METHOD

So it would seem that this roundabout method is the same in effect except that it circumvents that roadblock. Now that's interesting. I haven't ventured beyond 7*10 yet, but perhaps I will at some point.