The Magic of Binary Trains
A Childhood game of Numbers..
I was spellbound by this little game as a kid.. My father could read my mind instantly.. The surreal feel of magic and wonder ..
Think of a number between 1 and 31..
Here are the 5 houses. A B C D E..
House A: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31
House B: 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31
House C: 4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31
House D: 8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31
House E: 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31
~
Is your number in A? In B? In C? In D? In E?
And.. This is your number..
No big deal.. ust add the first number of each row where the number is present. Like 14 is in B, C, D ie 2 + 4+ 8 =14..
With passing years, this little game kept surprising me. High School math revealed.. this was the premise of binary system of numbers.
College told me.. this was the language of Computer Logic.. Everything encoded f 0s and 1s..
In the centenary celebrations of Bhaskaracharya.. when kids of the apartment were very young.. magic could still charm them.. Why bore the children with serious math.. I taught them this trick along with other magical feats with math.
In BR Hills, there was a Government School on looking our resort. With my broken Kannada and gestures, I remember teaching this game, and making the students decode the numbers.. I enjoyed every moment as much as the little kids.
I had a colleague with literature back ground.. What better way to intrigue her with Binary Numbers than this game.. And recently, as though Heavens wanted it.. A Schoolmate who is an arts teacher. I meet her after 30 plus years. She was talking so much about math that I was prompted to show her this trick. And she was delighted like a child.. May be Art and Mathematics are so connected..
On constructing this series.. she wanted to know in a very simple language.
Each line starts with a power of 2. {1, 2, 4, 8, 16, 32, 64} so on.. Previously we capped the guessing at 31 which was the highest number possible with {1, 2, 4, 8, 16}
Let us build the series for guessing a number till 15 [16 -1] using {1, 2, 4, 8} as the starting number of each home..
Like modulo counters, each row keeps incrementing X times, followed by a gap of X.. And the last number should be 15 in each list..Yup!
Home A: 1, [skip a number], 3, [skip a number],…. 15
Home B: 2, 3, [skip 2 numbers], 6, 7, [skip 2 numbers].. 15
Home C: 4, 5, 6, 7, [skip 4 numbers] 12, 13, 14, 15
Home D: 8, 9, 10, 11, 12, 13, 14, 15
While learning about Sanskrit Meters in Chants, I was dumb founded again. Binary choice of syllables. The Long and short lenghted ones.. Binary system was the very premise of the combination of meters..
Like my friend says.. Sometimes.. Memories age better with time!
