from Amazon
Wednesday, November 30, 2011
Bobby V. IV
Rangers, Mets, Lotte Marines, and now his fourth team, the Redsox. A compilation of reactions can be found here.
***
Anyway, I found this story:
“Ichiro is a mathematical genius,’’ he told me. “Because of that, he can read the angles of the field better than everyone else. When he runs to a spot in right field to make a catch, and the ball is there, waiting for him, it’s because he can see the angles better than anyone. I was in an elevator with him once. It was about a 40-floor hotel. He looked at the right side of the elevator, the even numbers, and added them up in his head in, like, two seconds.’’
There’s a little trick I like to play. It looks mighty impressive, even if it’s not. I can divide any number by 7, and get the answer to six decimal places. The trick is that the sequence after the decimal is always of the pattern 142857, and it loops back. So, 1/7 is .142857 and repeats. For 2/7, you start with the second smallest digit, and follow the same pattern: .285714. 3/7 starts with 4 (the third smallest digit), so you get .428571. And so on.
Even remembering the 6-digit sequence is easy enough. Double 7 (14), double that (28), double that and add 1 (57). So, once you have that 142857 sequence, you can divide any number by 7. Cute, right?
***
We know about adding all the numbers in sequence starting from 1, which is just n*(n+1)/2. The (n+1)/2 is simply the average of a sequence from 1 to n. And n is the count of numbers from 1 to n.
The Ichiro trick limits us to just the even numbers. In that case, instead of “n” in the above equation, we have “n/2”. That gives us the count. And instead of “n+1” over 2, it’s “n+2” over 2, which is the average between the maximum number and 2. So, we have n/2 * (n+2)/2.
We can further expand that to (n/2 * n/2) + n/2.
For odd numbers, it’s even easier (where n is the largest even number). The count remains at n/2, and the average is n-1 (to get your max odd number) plus 1, divided by 2, or n/2. So, simply n/2 squared.
To recap: adding up the odd numbers is n/2 squared. Adding up the even numbers is n/2 squared, plus n/2.
Therefore, adding up 1 through 40 is: 40*41/2 = 820
Limiting to odd numbers: 40/2 squared = 400
And to even numbers: 40/2 squared + 40/2 = 420
So, next time you see Bobby V in an elevator, you’ll know how to break the ice.
***
Are there little numeric “tricks” that you guys enjoy doing? I’d love to hear them.
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